UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Operations research for small business Ney, Hugh D. W. 1968

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1968_A4_5 N48.pdf [ 7.35MB ]
Metadata
JSON: 831-1.0093552.json
JSON-LD: 831-1.0093552-ld.json
RDF/XML (Pretty): 831-1.0093552-rdf.xml
RDF/JSON: 831-1.0093552-rdf.json
Turtle: 831-1.0093552-turtle.txt
N-Triples: 831-1.0093552-rdf-ntriples.txt
Original Record: 831-1.0093552-source.json
Full Text
831-1.0093552-fulltext.txt
Citation
831-1.0093552.ris

Full Text

OPERATIONS RESEARCH FOR SMALL BUSINESS by HUGH D. W. NEY B.A.Sc, University of B r i t i s h Columbia, 1962 M.A.Sc, University of B r i t i s h Columbia, 1964 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF BUSINESS ADMINISTRATION i n the Faculty of Commerce and Business Administration We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA July, 1968 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r a n . a dvan c ed deg ree a t the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I ag r ee t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and S t u d y . I f u r t h e r ag ree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r po s e s may be g r a n t e d by the Head o f my Depar tment o r by hits r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l no t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Depar tment o f COMMERCE  The U n i v e r s i t y o f B r i t i s h Co lumb ia Vancouve r 8, Canada Date JUT.Y, 1 Q68 ABSTRACT T h i s study i s concerned w i t h the p r a c t i c a b i l i t y of u s i n g o p e r a t i o n s r e s e a r c h i n a smal l business. For purposes of the study, o p e r a t i o n s r e s e a r c h i s regarded as a separate management f u n c t i o n f o r a p p l y i n g s c i e n t i f i c methods to the understanding o f the o p e r a t i o n s of g o a l - d i r e c t e d o r g a n i z a t i o n s . A s m a l l business i s d e f i n e d w i t h r e g a r d to the s i z e of i t s o p e r a t i o n s as having a v a l u e added of l e s s than f i v e m i l l i o n d o l l a r s per year. An examination of r e c e n t surveys demonstrates t h a t o p e r a t i o n s r e s e a r c h i s a p r e v a l e n t , growing and v a l u a b l e management a i d i n l a r g e and medium s i z e d companies. They a l s o p r o v i d e evidence t h a t OR i s not used e x t e n s i v e l y i n sm a l l b u s i n e s s . On the other hand, s t a t i s t i c s on business f a i l u r e s and r e p o r t s of r e s e a r c h on the management of s m a l l companies p r o v i d e evidence t h a t s m a l l businesses have man-agement problems which p o s s i b l y c o u l d be s o l v e d by o p e r a t i o n s r e s e a r c h . A survey of l o c a l s m a l l business management was con-ducted p r i n c i p a l l y to determine the extent to which o p e r a t i o n s r e s e a r c h i s used by smal l companies, the reasons f o r non-use of OR by most s m a l l businesses and the e x i s t e n c e of o p e r a t i n g problems which might be e f f e c t i v e l y s o l v e d by o p e r a t i o n s r e s e a r c h . i v T h i s survey, as w e l l as other evidence i n d i c a t e s t h a t o p e r a t i o n s r e s e a r c h i s used to a very l i m i t e d extent by s m a l l b u s i n e s s . The reasons f o r non-use a r e : 1) the n o n - a n a l y t i c a l approach of s m a l l business management, 2) the managers* l a c k of f a m i l i a r i t y w i t h o p e r a t i o n s r e s e a r c h , 3) the l a c k of t r a i n e d p e r s o n n e l , 4) the u n a v a i l a b i l i t y of accurate, r e l e v a n t data, 5) the h i g h c o s t o f l e a s i n g and o p e r a t i n g e l e c t r o n i c computers and 6) the o p i n i o n t h a t OR i s not economical f o r smal l b u s i n e s s . T h i s survey and oth e r r e s e a r c h has i d e n t i f i e d s m a l l b u s i n e s s problems to which OR might e f f e c t i v e l y be a p p l i e d . R e t a i n i n g c o n s u l t a n t s i s a means of overcoming the l a c k of t r a i n e d personnel e s p e c i a l l y i f the s m a l l business maintains a c o n t i n u i n g r e l a t i o n s h i p w i t h a c o n s u l t a n t who has a s m a l l , f l e x i b l e o p e r a t i o n and the a b i l i t y to a s s i s t i n other management f u n c t i o n s . Computer tim e - s h a r i n g and computer s e r v i c e bureaus are inexpensive means of o b t a i n i n g the computer c a p a b i l i t y which i s o f t e n necessary f o r o p e r a t i o n s r e s e a r c h . Small computers may a l s o be f e a s i b l e f o r a smal l business i f i t has enough ot h e r d a t a p r o c e s s i n g work. A case study of a l o c a l s m a l l business i d e n t i f i e d s a l e s f o r e c a s t i n g , c a p i t a l budgeting, p r o d u c t i o n s c h e d u l i n g and i n v e n t o r y c o n t r o l as areas i n which o p e r a t i o n s r e s e a r c h c o u l d p o s s i b l y c o n t r i b u t e towards the Company's g o a l s . V Formulation and t e s t i n g of d e c i s i o n r u l e s f o r i n v e n t o r y management and e s t i m a t i o n o f the c o s t s of an i n v e n t o r y c o n t r o l system f o r the Company demonstrate t h a t o p e r a t i o n s r e s e a r c h i s p r a c t i c a l f o r t h i s s m a l l b u s i n e s s . TABLE OF CONTENTS CHAPTER PAGE I. INTRODUCTION 1 T h e s i s Statement . . 1 The D e f i n i t i o n o f Operations Research 2 The D e f i n i t i o n of Small Business 7 Purpose and Scope of T h i s Study 9 I I . THE PREVALENCE OF OR IN INDUSTRY AND THE MANAGEMENT NEEDS OF SMALL BUSINESS 1 2 Operations Research i n Industry . 1 3 The Need f o r Greater E f f i c i e n c y i n Small Business 2 0 I I I . THE USE OF OPERATIONS RESEARCH IN SMALL BUSINESSES INCLUDING A SURVEY OF LOCAL EXPERIENCE 2 6 The Survey of L o c a l Small Businesses 2 7 The Extent and Success of Use of Operations Research 2 9 Reasons Why Operations Research i s not Used E x t e n s i v e l y i n Small Business 3 3 Small Business Problems f o r OR k6 IV. CONSULTANTS AND COMPUTERS 4 9 OR Consultants f o r Small Businesses 5 0 Computer S e r v i c e s f o r Small Businesses 5 5 v i i CHAPTER PAGE V. - A CASE STUDY: OPERATIONS RESEARCH FOR A SMALL COMPANY 68 A Description of the Company's Business . . . 69 A Description of the Company 71 Operating Problems 76 Inventory Study 84 Operations Research i n Other Areas 123 VI. SUMMARY AND CONCLUSIONS 128 BIBLIOGRAPHY 137 APPENDIX I: Questionnaire Used i n Survey of Local Small Businesses 142 APPENDIX I I : Generating Material Requirements Using a Matrix Formulation 14-5 APPENDIX I I I : Calculation of Present Value of Proposed Inventory Control System 151 LIST OP TABLES TABLE PAGE I. Surveys of the Number of American Companies Using OR 15 I I . Reasons f o r Non-Use of OR 18 I I I . Causes of Business F a i l u r e s i n The United St a t e s f o r 1967 22 IV. Companies and Managers Represented i n the Survey . . . . . . . . . . . 28 V. Summary of the R e s u l t s of the Survey 34 VI. Time-Sharing Costs 63 V I I . Inventory Items f o r D e t a i l e d Study . 89 V I I I . Ordering Cost 93 IX. Reserve Stock D e c i s i o n Table 101 X. Inventory S i m u l a t i o n - Item A . 104 XI. Comparison of R e s u l t s of A c t u a l and Simulated Inventory C o n t r o l 121 X I I . Net Present Value C a l c u l a t i o n of the Proposed Inventory C o n t r o l System . . . . . . 152 ACKNOWLEDGEMENTS A c o n s i d e r a b l e amount of the i n f o r m a t i o n f o r t h i s study was gained i n c o n v e r s a t i o n s w i t h s m a l l business managers, computer s e r v i c e personnel and c o n s u l t a n t s . The author i s p a r t i c u l a r l y Indebted to the managers of companies t h a t are r e p r e s e n t e d i n the survey who gave up to three hours of t h e i r v a l u a b l e time. No names w i l l be mentioned as many wished to remain anonymous. Mr. Morris C'arley of Kates, Peat, Marwick Company, Messrs. W. Tennant and D. Bowman of Computech C o n s u l t i n g Canada L t d . are c o n s u l t a n t s who p r o v i d e d v a l u a b l e .information. The per-sonnel a t EDP Data Centers, L t d . and Westcoast Data Pro-c e s s i n g co-operated as d i d Messrs. J . K i n v l g of Univac and D. MacDonald and J . Laak of IBM. The author i s a l s o indebted to h i s a d v i s o r s s , Dr. J . S w i r l e s , P r o f e s s o r H. W i l k i n s o n and P r o f e s s o r D. F i e l d s . Having acknowledged the a s s i s t a n c e of o t h e r s , my wife can not be ignored f o r t y p i n g many d r a f t s and p r o v i d i n g con-s i d e r a b l e encouragement. CHAPTER I INTRODUCTION I. THESIS STATEMENT The i n c r e a s i n g i n t e r e s t i n o p e r a t i o n s r e s e a r c h by-l a r g e companies has r a i s e d the q u e s t i o n of i t s r e l e v a n c e to 1 2 s m a l l b u s i n e s s e s . ' In t h i s r e g ard i t i s the purpose of t h i s study to examine the f o l l o w i n g p r o p o s i t i o n s : 1) Small b u s i n e s s e s do not g e n e r a l l y use o p e r a t i o n s r e s e a r c h as an a i d to management. 2) The main reasons why o p e r a t i o n s r e s e a r c h i s not used more e x t e n s i v e l y i n s m a l l businesses are a l a c k of knowledge among s m a l l b u s i n e s s managers as to the scope, techniques and v a l u e of OR^ and the u n a v a i l a b i l i t y of competent, t r a i n e d personnel f o r doing the o p e r a t i o n s a n a l y s i s . 3) Operations r e s e a r c h c o u l d be used f o r more e f f e c t i v e management of smal l b u s i n e s s e s i n many i n s t a n c e s . Both 'operations r e s e a r c h ' and 'small b u s i n e s s ' are terms which have r a t h e r broad and v a r i e d meanings. Therefore they w i l l be d e f i n e d f o r purposes of t h i s study. D.B, Hertz, "Progress of I n d u s t r i a l Operations Research i n the U.S.," ( 1 9 5 7 ) . p. 4 6 7 . (See B i b l i o g r a p h y f o r d e t a i l s of p u b l i c a t i o n ) . 2 R.S. Gander, "The State of O p e r a t i o n a l Research i n the U n i t e d Kingdom," (1957), p. 512. 3 OR w i l l be used i n t e r c h a n g e a b l y with, and, as an a b b r e v i a t i o n f o r o p e r a t i o n s r e s e a r c h . 2 I I . THE DEFINITION OF OPERATIONS RESEARCH The v e r y f a c t t h a t so much i s w r i t t e n concerning the meaning and scope of o p e r a t i o n s r e s e a r c h suggests t h a t there i s c o n s i d e r a b l e c o n f u s i o n as to i t s d e f i n i t i o n . Some b u s i n e s s -men and s c i e n t i s t s regard i t as the a p p l i c a t i o n of s t a t i s t i c s and common sense to business problems. To many o p e r a t i o n s r e s e a r c h e r s , OR i s a comprehensive f u n c t i o n i n c l u d i n g many othe r management s e r v i c e s such as systems a n a l y s i s , market 4 r e s e a r c h and i n d u s t r i a l e n g i n e e r i n g . To many s t a f f groups, i t i s the development of new t o o l s o f a n a l y s i s to be used i n t h e i r p a r t i c u l a r a r e a of management s e r v i c e . For i n s t a n c e , accountants c l a i m OR techniques as p a r t of t h e i r k i t of t o o l s as do I n d u s t r i a l engineers and systems a n a l y s t s . These views of o p e r a t i o n s r e s e a r c h are wid e l y d i f f e r e n t and hence i t can not be s a i d t h a t there i s a g e n e r a l l y accepted d e f i n i t i o n of o p e r a t i o n s r e s e a r c h . Even i n the d e f i n i t i o n s g i v e n by a u t h o r i t i e s i n the f i e l d of OR there i s a c o n s i d e r a b l e divergence. For i n s t a n c e S t a r r and M i l l e r regard OR as " a p p l i e d d e c i s i o n theory"-' and there i s much to commend t h i s concept o f OR. A s i m u l a t i o n P.J. Robinson, " O p e r a t i o n a l Research i n Canada," (1957), p. 469. ->M.K. S t a r r , and D.W. M i l l e r , Executive D e c i s i o n s and  Operations Research. (I960), p. 104. 3 model i s an example i n t h a t i t t e s t s a l t e r n a t i v e s to s e l e c t the one which g i v e s the h i g h e s t expected reward i n terms of o r g a n i z a t i o n a l g o a l s . However t h i s concept tends to make OR r a t h e r broad, f o r i t co u l d then i n c l u d e many aspects o f accounting, i n d u s t r i a l e n g i n e e r i n g , e t c . On the other hand S t a f f o r d Beer regards o p e r a t i o n a l r e s e a r c h as the a p p l i c a t i o n of s c i e n c e to the a n a l y s i s of a c t i v i t y , ^ which again i s q u i t e broad. Our purpose here i s to d e f i n e OR as a p a r t i c u l a r management s e r v i c e i n p a r a l l e l r e l a t i o n s h i p w i t h accounting, systems a n a l y s i s , f i n a n c e , i n d u s t r i a l e n g i n e e r i n g and market r e s e a r c h , and to determine i f , by d e f i n i t i o n , o p e r a t i o n s r e s e a r c h i s a p p l i c a b l e to smal l b u s i n e s s e s . The f o l l o w i n g d e f i n i t i o n , which probably i s not g e n e r a l l y 7 accepted, i s based on the d e f i n i t i o n s of Herrman and Magee and Ackoff, l e a d i n g a u t h o r i t i e s i n the f i e l d of OR, and p r o v i d e s a b a s i s f o r d e f i n i n g the boundaries of o p e r a t i o n s r e s e a r c h as a management s e r v i c e . S t a f f o r d Beer, "Cybernetics and O p e r a t i o n a l Research," (1959). P. 12. 7 C C . Herrman, and J.P. Magee, "Operations Research f o r Management," (1963). pp. 23-29. 8R.L. Ackoff, "The Meaning, Scope and Methods of Operations Research," (I96l), pp. 1-34. 4 Operations r e s e a r c h i s , as i t s name i m p l i e s , r e s e a r c h on the o p e r a t i o n s of o r g a n i z a t i o n s , i n v o l v i n g a p a r t i c u l a r k i n d of r e s e a r c h , a p a r t i c u l a r view of o p e r a t i o n s and a o d e f i n i t e concept of o r g a n i z a t i o n s . Thus i t i s necessary to d e f i n e these terms as used i n t h i s r e gard. The 'research* r e f e r r e d to above i s the a p p l i c a t i o n of the ' s c i e n t i f i c method' to d i s c o v e r an u n d e r l y i n g mechanism i n the system or o r g a n i z a t i o n which g i v e s r i s e to the observed facts.^° In t h i s context, r e s e a r c h i s not s o l e l y concerned w i t h the f o r m u l a t i o n of new, g e n e r a l l y a p p l i c a b l e techniques and the a l g o r i s m s f o r t h e i r s o l u t i o n , even though t h i s p a r t i c u l a r aspect occupies by f a r the g r e a t e s t p r o p o r t i o n of the OR l i t e r a t u r e . Rather, because f o r p r a c t i c a l purposes each business o r g a n i z a t i o n i s unique, the r e s e a r c h r e f e r r e d to here a p p l i e s to the study o f the i n t e r a c t i n g v a r i a b l e s of a p a r t i c u l a r system or p a r t of the o p e r a t i o n . S p e c i f i c a l l y , the o p e r a t i o n s r e s e a r c h e r b u i l d s a model of the system by the a p p l i c a t i o n of s c i e n t i f i c techniques, i n c l u d i n g mathematical m a n i p u l a t i o n , which i s u s e f u l f o r p r e d i c t i n g Herrman, and Magee, op_. c i t . , p. 23 1 0C.P. Goodeve, "The S c i e n t i f i c Method," (1957), p. 18. 5 i t s behaviour under d i f f e r e n t environments and d e c i s i o n a l t e r n a t i v e s - a means of c l a r i f y i n g the r e l a t i o n s h i p between a c t i o n s and t h e i r outcomes.'^ Thus, as Herrman and Magee s t a t e ; "The a p p l i c a t i o n o f the s c i e n t i f i c a t t i t u d e and the a s s o c i a t e d techniques to the study o f o p e r a t i o n s , - - - , i s what i s i m p l i e d by o p e r a t i o n s r e s e a r c h . " 1 2 Prom Ac k o f f we l e a r n t h a t , "An 'o p e r a t i o n ' i s a set of a c t s r e q u i r e d f o r the accomplishment of some d e s i r e d outcome; t h a t i s , i t i s not a s i n g l e a c t but a complex of a c t s ( i n v o l v i n g the p o s s i b i l i t y o f c h o i c e s ) performed s i m u l t a n e o u s l y o r i n sequence, which l e a d to the accomplish-13 ment of some d e s i r e d outcome." J But OR i s not concerned w i t h a l l types of o p e r a t i o n s . For i n s t a n c e , the o p e r a t i o n of an i n d i v i d u a l who 'operates' a machine i s the concern of i n d u s t r i a l engineers, not of o p e r a t i o n s r e s e a r c h e r s . A c k o f f s t a t e s t h a t o p e r a t i o n s r e s e a r c h i s concerned w i t h "^G.M. Pe r r e r o d i R o c c a f e r r e r a , Operations Research Models f o r Business and Industry, (1964), p.. 17. 12 Herrman, and Magee, op, c i t . , p. 24. •^Ackoff, op_. c i t . . p. 8 ( f o r a more formal d e f i n i t i o n of 'operation* see Ackoff, op_. c i t . , pp. 9-10) 6 the o p e r a t i o n s o f o r g a n i z a t i o n s where: "an o r g a n i z a t i o n can be d e f i n e d as a p u r p o s e f u l system w i t h f o u r e s s e n t i a l c h a r a c t e r i s t i c s : 1) Some of i t s components are human beings; 2) R e s p o n s i b i l i t y f o r c h o i c e s ( a l t e r n a t i v e ) a c t s i s d i v i d e d among two or more i n d i v i d u a l s . 3) The f u n c t i o n a l l y d i s t i n c t sub-groups are aware of each ot h e r ' s c h o i c e s e i t h e r through communication or o b s e r v a t i o n . 4) A sub-group of i n d i v i d u a l s i n the o r g a n i z a t i o n has a c o n t r o l f u n c t i o n - norm a l l y an ex e c u t i v e body. T h i s d e f i n i t i o n suggests t h a t many smal l businesses would not be s u i t a b l e s u b j e c t s f o r o p e r a t i o n s r e s e a r c h , i n t h a t r e s p o n s i b i l i t y f o r c h o i c e s i s not d i v i d e d and o f t e n the same i n d i v i d u a l or group t h a t e x e r c i s e s the c o n t r o l f u n c t i o n a l s o makes a l l the d e c i s i o n s . In deed, complexity of system or o r g a n i z a t i o n i s o f t e n h e l d as an e s s e n t i a l f e a t u r e o f o p e r a t i o n s r e s e a r c h . M a n y sma l l businesses c o n s i s t o f an i n d i v i d u a l p r o p r i e t o r who manages the business by h i m s e l f . Such a business a p p a r e n t l y would not be a s u i t a b l e s u b j e c t f o r o p e r a t i o n s r e s e a r c h . Thus we have I b i d . , pp. 11-12 -^o. Solandt, "Observation, Experiment, and Measure-ment i n Operations Research," ( 1955 ) . P. 4 ^•^Perrero d i Roccaf e r r e r a , l o c . c i t . 7 pla c e d a lower bound on the ' s i z e ' of business to which o p e r a t i o n s r e s e a r c h i s a p p l i c a b l e . T h i s bound i s d e f i n e d by the e x i s t e n c e of more than one f u n c t i o n a l sub-group which makes d e c i s i o n s a f f e c t i n g the achievement of o r g a n i z a t i o n a l o b j e c t i v e s , and the e x i s t e n c e of a c o n t r o l sub-group which compares achieved outcomes w i t h d e s i r e d outcomes. Any business t h a t does not have these o r g a n i z a t i o n a l sub-groups we accept as being i n a p p r o p r i a t e f o r the a p p l i c a t i o n of o p e r a t i o n s r e s e a r c h , based on the above d e f i n i t i o n of o p e r a t i o n s r e s e a r c h . I I I . THE DEFINITION OF SMALL BUSINESS 'Small b u s i n e s s ' i s a term used i n a wide v a r i e t y of contexts and t h e r e f o r e i t too has no g e n e r a l l y accepted d e f i n i t i o n . Some a u t h o r i t i e s have suggested t h a t s m a l l b usiness can be g e n e r a l l y d e s c r i b e d i n terms of q u a l i t a t i v e c o n s i d e r a t i o n s . For i n s t a n c e ; a) the c o n t r o l l i n g owners are u s u a l l y the managers; b) few, i f any s p e c i a l i z e d p r o f e s s i o n a l s t a f f members are a v a i l a b l e to execute separate management f u n c t i o n s ; c) r e s e a r c h f a c i l i t i e s are l a c k i n g ; d) the business i s self-dependent (which i s not e n t i r e l y synonymous wi t h independent); are some of the suggested c h a r a c t e r i s t i c s of smal l 8 17 b u s i n e s s e s . Although these h o l d as g e n e r a l c o n s i d e r a t i o n s of t h i s study, a more q u a n t i t a t i v e d e f i n i t i o n i s deemed necessary. In the United S t a t e s , the Small Business A d m i n i s t r a -t i o n (SBA) employs a v a r i e t y o f standards. For government purchasing i n c e n t i v e s , a s m a l l business g e n e r a l l y has l e s s than 500 employees, but I t v a r i e s depending on the i n d u s t r y . By example, a s m a l l b u s i n e s s i n the f l a t g l a s s i n d u s t r y has l e s s than 1000 employees. For SBA l o a n purposes a smal l b u s i n e s s has l e s s than 250 employees although a g a i n i t v a r i e s among I n d u s t r i e s . For purposes of t h i s study a business i s smal l r e l a t i v e to the l a r g e companies employing f u l l - t i m e OR s t a f f s and t h e r e f o r e a 'small business* by our d e f i n i t i o n may be somewhat l a r g e r than f o r oth e r purposes. A l s o the measure should approximate the s i z e of the o p e r a t i o n and, f o r t h i s reason, v a l u e added has been s e l e c t e d as a measure of s i z e . To o b t a i n a maximum l i m i t on the value added f o r a sma l l b u s i n e s s , the f o l l o w i n g c a l c u l a t i o n i s made. I f we accept as s m a l l a business employing 350 people, approximate the l a b o u r c o s t a t $ 8 , 0 0 0 per man year and F.X. Wildgen, F i n a n c i n g Small Business. ( 1 9 6 2 ) , p. 3 9 assume t h a t the sum of d e p r e c i a t i o n , i n t e r e s t , taxes and p r o f i t approximately equal l a b o u r c o s t s , then a small b u s i n e s s w i l l have a value added of f i v e m i l l i o n d o l l a r s per year or l e s s . In t h i s study we are t h e r e f o r e concerned w i t h those businesses which have a va l u e added of l e s s than f i v e m i l l i o n d o l l a r s per year, but whose o p e r a t i n g d e c i s i o n s are made by more than one person w i t h the knowledge of each o t h e r s a c t i o n s and w i t h o v e r a l l c o n t r o l e x e r c i s e d by a sub-group of the business management. IV. PURPOSE AND SCOPE OP THIS STUDY The apparent success of o p e r a t i o n s r e s e a r c h as an a i d to p l a n n i n g and c o n t r o l i n l a r g e o r g a n i z a t i o n s has c r e a t e d an i n t e r e s t i n a p p l y i n g i t to small business management. For i n s t a n c e , the United S t a t e s Small Business A d m i n i s t r a t i o n has sponsored r e s e a r c h i n t h i s a r e a and has a l s o i s s u e d a " T e c h n i c a l A i d " on o p e r a t i o n s r e s e a r c h f o r s m a l l b u s i n e s s managers. As regards the l o c a l s i t u a t i o n , t h e r e are many smal l manufacturers, d i s t r i b u -t o r s , and ot h e r s m a l l businesses i n B r i t i s h Columbia • .... . W.J. Gave11, Operations A n a l y s i s i n Small Manu- f a c t u r i n g Firms, (I963T. : ~ which c o u l d perhaps use o p e r a t i o n s r e s e a r c h to i n c r e a s e t h e i r v i a b i l i t y and growth p r o s p e c t s and t h e r e f o r e a s s i s t the development of l o c a l secondary i n d u s t r y . In t h i s r e gard, a number of l o c a l c o n s u l t a n t s have expressed t h e i r i n t e r e s t from the p o i n t of view of the market f o r t h e i r s e r v i c e s i n o p e r a t i o n s r e s e a r c h . With t h i s i n mind, i t i s the purpose of t h i s study to examine the v a l i d i t y of the three p r o p o s i t i o n s s t a t e d a t the beginning of t h i s chapter. In g e n e r a l , to what extent i s o p e r a t i o n s r e s e a r c h f e a s i b l e f o r s m a l l businesses? Obviously t h i s q u e s t i o n can o n l y be answered f o r a s p e c i f i c s i t u a t i o n and t h e r e f o r e much of the f o l l o w i n g d i s c u s s i o n w i l l be concerned w i t h i d e n t i f y i n g the f a c t o r s which tend to h i n d e r the s u c c e s s f u l use of OR by smal l businesses, and w i t h suggesting how these hindrances might be overcome. Some evidence to support the sugg e s t i o n t h a t there i s a need f o r OR i n smal l businesses i s pro v i d e d i n the f o l l o w i n g chapter. T h i s i n c l u d e s s t a t i s t i c s on business f a i l u r e s and t h e i r causes, and some r e s u l t s o f surveys on the extent, growth and va l u e o f o p e r a t i o n s r e s e a r c h i n i n d u s t r y . Chapter I I I d i s c u s s e s the r e s u l t s o f a survey of l o c a l s m a l l businesses conducted by the author. To a l a r g e extent i t d e a l s w i t h the d i f f i c u l t i e s of u s i n g OR i n s m a l l b u s i n e s s e s . Two of these are the l a c k of t r a i n e d 11 per s o n n e l , and the hig h c o s t of l e a s i n g e l e c t r o n i c computers. In Chapter IV assessment w i l l be made of the s e r v i c e s of c o n s u l t a n t s and the v a r i o u s methods f o r o b t a i n i n g e l e c t r o n i c computer c a p a b i l i t y as means of r e d u c i n g these d i f f i c u l t i e s . F i n a l l y , a case study of a smal l manufacturer w i l l be the s u b j e c t of Chapter V. In p a r t i c u l a r , the i n v e n t o r y problems of t h i s company are studied from an OR standpoint as an example of the a p p l i c a t i o n of o p e r a t i o n s r e s e a r c h to smal l b u s i n e s s e s . CHAPTER I I THE PREVALENCE OP OR IN INDUSTRY AND THE MANAGEMENT NEEDS OP SMALL BUSINESS The purpose of t h i s chapter i s to determine the degree to which i n d u s t r y has engaged i n o p e r a t i o n s r e s e a r c h as an a i d to management, and to assess i f s m a l l b u s i n e s s e s have a need f o r o p e r a t i o n s r e s e a r c h . In other words, an attempt i s made to i n d i c a t e why smal l business should be I n t e r e s t e d In o p e r a t i o n s r e s e a r c h . In t h i s chapter we demonstrate by r e v i e w i n g the r e s u l t s of v a r i o u s surveys t h a t o p e r a t i o n s r e s e a r c h i s used by a s i g n i f i c a n t p r o p o r t i o n of l a r g e companies i n Canada, Great B r i t a i n , and the United S t a t e s of America. These surveys a l s o show t h a t o p e r a t i o n s r e s e a r c h may be a u s e f u l a i d to management and t h a t i t s importance i s growing. As to whether or not smal l business r e q u i r e s o p e r a t i o n s r e s e a r c h can o n l y be answered In a p a r t i c u l a r case (see Chapter V.) However, i t was c o n s i d e r e d t h a t s t a t i s t i c s on p i r o d u c t i v i t y and p r o f i t a b i l i t y as a f u n c t i o n o f company s i z e and the reasons f o r the h i g h f a i l u r e r a t e o f smal l f i r m s might I n d i c a t e t h a t s m a l l businesses do r e q u i r e management a i d s such as o p e r a t i o n s r e s e a r c h . The degree to which the r e a d i l y a v a i l a b l e l i t e r a t u r e demonstrates t h i s need w i l l 13 be d i s c u s s e d i n t h i s chapter. I. OPERATIONS RESEARCH IN INDUSTRY The importance and growth of o p e r a t i o n s r e s e a r c h i n Ind u s t r y s i n c e the Second World War has been suggested by surveys of i n d u s t r i a l management of which the ones by H e r t z 1 , V a i r t e r 2 , Schumacher and Smith^, R i v e t t \ Robinson^, and Gander^, were examined p a r t i c u l a r l y with r e s p e c t to s i z e of company and the value o f the r e s u l t s . U n f o r t u n a t e l y , none of the r e s u l t s of the surveys can be assumed to be random samples so t h a t no d e f i n i t e c o n c l u s i o n s can be drawn as to the p r o p o r t i o n o f companies, even of a p a r t i c u l a r type or D.B. Hertz, "Progress o f I n d u s t r i a l Operations Research i n the U.S.," (1957), PP. 455-468 o W.J. V a t t e r , "The Use of Operations Research i n American Companies," (1967), PP. 721-730. ^C.C. Schumacher, and B.E. Smith, "Sample Survey of I n d u s t r i a l Operations Research A c t i v i t i e s , " (1965), pp. 1023-1027. 4 B.H.P. R i v e t t , "A Survey of O p e r a t i o n a l Research i n B r i t i s h I n d u s t r y , " (1959). pp. 189-205. -*P. J . Robinson, " O p e r a t i o n a l Research i n Canada, " (1957), PP. 469-490; ^R.S. Gander, "The State of O p e r a t i o n a l Research i n the United Kingdom," (1957). pp. 500-513. s i z e category, which are engaged i n o p e r a t i o n s r e s e a r c h because the mere f a c t of v o l u n t a r y response r e p r e s e n t s a b i a s . A l s o , the c h a r a c t e r i s t i c s of those surveyed were d i f f e r e n t i n each case. However, the surveys do p r o v i d e evidence t h a t OR i s an important and growing a c t i v i t y i n I n d u s t r y . OR A c t i v i t y i n American i n d u s t r y Table I summarizes the r e s u l t s of three surveys on the extent of OR a c t i v i t y i n American companies. In a l l cases the q u e s t i o n n a i r e s were sent to d i f f e r e n t p o p u l a t i o n s and the response l e v e l was f a i r l y low. In the survey by Hertz, a q u e s t i o n n a i r e was sent to 5»325 i n d i v i d u a l s comprising the e n t i r e membership of OR o r i e n t e d s o c i e t i e s and of p r e s i d e n t s of American companies w i t h more than one thousand employees. The survey i s thus b i a s e d by p a r t i c u l a r l y i n c l u d i n g people who have an obvious i n t e r e s t i n OR. Schumacher and Smith' survey i n c l u d e d the 168 companies of Fortune's 'Top 500' i n d u s t r i a l s which were seeking to employ mathematicians and engineers as evidenced by t h e i r advertisements i n the 1964 United S t a t e s " C o l l e g e Placement Manual". Obviously 1 5 TABLE I SURVEYS OF THE NUMBER OF AMERICAN Hertz Schumacher and V a t t e r n . ( . 1 9 5 7 ) ' Smith ( 1 9 6 . 4 ) 8 . . . ( . 1 9 . 6 7 V 1. Companies to 3 , 1 5 0 168 3 , 5 0 0 which q u e s t i o n -n a i r e s were sent 2 . Respondents 6 3 1 6 5 3 6 0 3 . Companies 3 2 4 4 9 2 3 7 ( 2 8 7 ) * 4 . Companies p l a n - 144 n i n g to use OR 5 . Percent Range 1 0 - 5 0 3 0 - 7 5 7 - 6 5 of OR users 6 . S u b j e c t i v e E s t - 20 6 0 3 5 imate of Percent of OR users 7 . Reported r e s u l t s good 7 5 not i n q u e s t i o n - 728** n a i r e f a i r 5 5 3 6 l * * poor not i n c l u d e d 5 2 * * u n c e r t a i n 167 I67*"* * i n c l u d e s ' i n f o r m a l ' u s e r s . i n c l u d e s r e s u l t s , f o r each technique used, see Page 17 7 Hertz, l o c . c i t . o Schumacher and Smith, l o c . c i t . 9 V a t t e r , l o c . c i t . 16 t h i s survey i s b i a s e d towards v e r y l a r g e companies i n t e r e s t e d i n doing q u a n t i t a t i v e a n a l y s i s . The companies to which V a t t e r sent h i s q u e s t i o n n a i r e r e p r e s e n t the most unbiased p o p u l a t i o n , but u n f o r t u n a t e l y , he obtained a v e r y poor response. The 3*500 companies surveyed were re p r e s e n t e d i n the F i n a n c i a l E x e c u t i v e s I n s t i t u t e by i n d i v i d u a l managers or as c o r p o r a t e members, the t o t a l of which made up the e n t i r e membership. With r e f e r e n c e to the contents of Table I, the "Percent Range of OR Users" was obtained on the low s i d e by assuming t h a t none of the non-respondents were engaged i n OR and on the upper l i m i t by assuming t h a t the respondents were a random sample of companies i n c l u d e d i n the survey. The s u b j e c t i v e estimate as to the percentage of OR users i n the p o p u l a t i o n t h a t was surveyed i s by the author based on h i s study of the r e s u l t s . The growth of OR a c t i v i t y i n The United States i s bare-- l y d e c e r n i b l e from the above surveys even though they cover a ten year p e r i o d of o b v i o u s l y , r a p i d l y growing i n t e r e s t i n OR. Comparison of the Hertz and V a t t e r surveys does p r o v i d e some evidence of growth e s p e c i a l l y c o n s i d e r i n g t h a t the 1957 survey was e s p e c i a l l y aimed a t people o b v i o u s l y i n t e r e s t e d i n OR whereas the 1967 survey was not. A d d i t i o n a l evidence of growth i s obtained from V a t t e r * s survey which enquired i n t o the l e n g t h of time the company had been 17 engaged i n OR a c t i v i t y . Of the 237 formal users, o n l y 60 had r e c o g n i z e d i t as a s p e c i f i c f u n c t i o n f o r more than f i v e year, t h a t i s , a g r e a t m a j o r i t y of companies have o n l y s t a r t e d u s i n g OR f o r m a l l y w i t h i n the l a s t f i v e years I The E f f e c t i v e n e s s of OR i n American I n d u s t r y The Hertz and V a t t e r surveys both enquired as to the respondent's e v a l u a t i o n of the OR work. For a s s e s s i n g r e s u l t s , Hertz suggested phrases such as " a p p r e c i a b l e s a v i n g s " and "too e a r l y to t e l l " so t h a t some i n t e r p r e t a t i o n was neces-s a r y to make them correspond to V a t t e r ' s terms (Table I.) A l s o the Hertz e v a l u a t i o n s apply to OR i n g e n e r a l usage by the company whereas V a t t e r ' s a p p l i e s to s p e c i f i c OR techniques, as used by each company. In o t h e r words, the numbers under V a t t e r i n Table I r e p r e s e n t the t o t a l of a l l techniques as used by a l l companies. The e v a l u a t i o n s were most l i k e l y made by respondents to the q u e s t i o n n a i r e who would g e n e r a l l y be i n s t a f f p o s i t i o n s , r a t h e r than by o p e r a t i n g managers and t h e r e f o r e they are no doubt b i a s e d . Even so, the surveys p r o v i d e support f o r o t h e r evidence, such as the c o n t i n u i n g i n t e r e s t i n OR, t h a t o p e r a t i o n s r e s e a r c h i s p r o v i n g e f f e c t i v e as an a i d to management. With t h i s evidence of g e n e r a l e f f e c t i v e n e s s the reasons f o r non-use of OR i s an i n t e r e s t i n g r e s u l t of 18 V a t t e r ' s survey i n t h a t i t approximately p a r a l l e l s evidence f o r non-use i n s m a l l b u s i n e s s e s as demonstrated i n Chapter I I I . (see Table I I ) . The r e s u l t s show the number of companies which gave each reason. The g e n e r a l a r e a of l a c k of e d ucation i s by f a r the main reason f o r not u s i n g OR. TABLE I I REASONS FOR NON-USE OF OR 1 0 .. Number of Companies 1. "Inadequate access to a p p r o p r i a t e equipment 31 2. "Lack of s u f f i c i e n t l y competent p e r s o n n e l " 103 3. "Lack of i n t e r e s t among o p e r a t i n g managers" 91 4. "Not a p p l i c a b l e to t h i s business a t a l l " 8 The Use of OR by S i z e of Firm i n the United S t a t e s In both the Hertz and Schumacher r e p o r t s there i s evidence t h a t o n l y l a r g e companies were surveyed. Only i n V a t t e r ' s survey was there a breakdown of usage by s i z e o f company. Of the seventy-seven companies wi t h s a l e s of l e s s than t w e n t y - f i v e m i l l i o n d o l l a r s , forty-two or approximately f i f t y - f i v e per cent r e c o g n i z e d OR as a spec-V a t t e r , op_0 c i t . , p. 728. 19 i f i c f u n c t i o n i n the o r g a n i z a t i o n as compared to e i g h t y per number of r e p l i e s from s m a l l business and the s p e c u l a t i o n t h a t non-respondents are l e s s l i k e l y to be OR us e r s , suggests t h a t a much s m a l l e r p r o p o r t i o n of s m a l l companies use OR, un l e s s of course the members of the F i n a n c i a l E x e c u t i v e s I n s t i t u t e are by and l a r g e employees of l a r g e companies. Operations Research A c t i v i t y i n Canada In 1957» Robinson suggested t h a t perhaps o n l y twenty-f i v e Canadian companies had or were b u i l d i n g o p e r a t i o n s 12 r e s e a r c h a c t i v i t i e s . He r e p o r t s on a U n i v e r s i t y o f West-ern Ontario survey which sent out q u e s t i o n n a i r e s to s i x t y -seven o r g a n i z a t i o n s thought to be u s i n g o p e r a t i o n s r e s e a r c h , o r to be i n t e r e s t e d i n the s u b j e c t . Of the f i f t y - t w o responding companies, on l y e l e v e n were u s i n g OR and another t h i r t e e n companies were c o n s i d e r i n g u s i n g i t . That t h i s s m a l l number of companies has a p p a r e n t l y i n c r e a s e d i s evidenced by the i n c r e a s i n g l e n g t h of the membership l i s t o f the Canadian O p e r a t i o n a l Research S o c i e t y . cent f o r a l l s i z e groups. 11 However, the r e l a t i v e l y s m a l l 11 I b i d p. 726 12-Robinson, op_. c i t . , pp. 469-480. Operations Research A c t i v i t y In B r i t a i n 20 The l i t e r a t u r e a p p a r e n t l y c o n t a i n s no r e c e n t survey t h a t i s aimed at e s t i m a t i n g the number of B r i t i s h f i r m s engaged i n o p e r a t i o n s r e s e a r c h . However, Gander 1-* d e s c r i b e s OR a c t i v i t y i n a number of important i n d u s t r i e s such as power, t r a n s p o r t , i r o n and s t e e l , e t c . I t appears from h i s a r t i c l e t h a t most of the l a r g e f i r m s i n these i n d u s t r i e s were u s i n g o p e r a t i o n a l r e s e a r c h by 1957 even i f they d i d not have a s p e c i f i c OR department. Many of the f o r m a l l y e s t a b l i s h e d OR departments are l a r g e , having up to f i f t y q u a l i f i e d people. Gander a l s o s t a t e s t h a t the membership of the O p e r a t i o n a l Research S o c i e t y t r i p l e d i n membership between 1953 and 1957. I I . THE NEED FOR GREATER EFFICIENCY IN SMALL BUSINESS The above f i n d i n g s i n d i c a t e t h a t s m a l l f i r m s do not use o p e r a t i o n s r e s e a r c h as e x t e n s i v e l y as l a r g e companies. The q u e s t i o n a r i s e s - Do they need o p e r a t i o n s r e s e a r c h ? In an attempt-to answer t h i s q u e s t i o n the l i t e r a t u r e was surveyed f o r i n f o r m a t i o n on p r o d u c t i v i t y , p r o f i t a b i l i t y and f a i l u r e r a t e as a f u n c t i o n of s i z e of f i r m . U n f o r t u n a t e l y -^Gander, l o c . c i t . 21 no Information on p r o d u c t i v i t y was obtained. However, there e x i s t s some r e s e a r c h on p r o f i t a b i l i t y , and a r t i c l e s on the need f o r improved management of smal l b u s i n e s s e s . As a s u b s t i t u t e f o r p r o d u c t i v i t y i n f o r m a t i o n , f a i l u r e r a t e s and the causes of f a i l u r e are examined to assess those areas where s m a l l business management i s weak and a s c e r t a i n i f OR has anything to o f f e r . Again no s t a t i s t i c s on f a i l u r e r a t e s by s i z e of f i r m were obtained but numbers of f a i l u r e by s i z e o f l i a b i l i t y i n d i c a t e (and i t seems g e n e r a l l y accepted) t h a t s m a l l f i r m s are v e r y s u s c e p t i b l e to f a i l u r e . - ^ ' For i n s t a n c e , i n 1966 approximately e i g h t y per cent of the t h i r t e e n thousand f a i l u r e s i n the United S t a t e s had l i a b i l -i t i e s o f l e s s than $ 1 0 0 , 0 0 0 . More r e l e v a n t to our study are the s t a t i s t i c s on causes of f a i l u r e s . Dun and B r a d s t r e e t s t a t i s t i c s f o r 1967 , based on the o p i n i o n of c r e d i t o r s and i n f o r m a t i o n i n c r e d i t r e p o r t s are g i v e n i n Table I I I . -^See monthly Issues of Dun's Review. ^ J . C . Worthy, "Who F a i l s and Why?" (1966) pp. 21-26 22 TABLE I I I CAUSES OF BUSINESS FAILURES IN THE UNITED STATES FOR I 9 6 7 I 6 Cause ...... - •- -Percentage of F a i l u r e s Neglect 3.1# Fraud 1A% Inexperience, Incompetence 92.5% Inadequate s a l e s Heavy o p e r a t i n g expenses R e c e i v a b l e s d i f f i c u l t i e s Inventory d i f f i c u l t i e s E x c e s s i v e f i x e d a s s e t s Poor l o c a t i o n Competitive weakness 39,9% 1 2 . 8 $ 9 . 9 ^ 6.2% ^.7% 3.2% 21.2% D i s a s t e r 1,0% Reason Unknown 1,1% These s t a t i s t i c s are c o r r o b e r a t e d by a survey of the causes of success and f a i l u r e of n i n e t y - f i v e Michigan manu-f a c t u r e r s t h a t were e s t a b l i s h e d i n the year ended 30 June, 1 9 6 0 . 1 ^ Of these f i r m s , t h i r t y - s e v e n were c l e a r successes and t h i r t y - s i x f i r m s f a i l e d . The d i f f e r e n c e between success l 6Rowena Wyant, "Business F a i l u r e s , " ( 1 9 6 8 ) , p. 119 I?"Why New Businesses Succeed," Nations Business, g 2 ( A p r i l 1 9 6 4 ) , pp. 5 6 - 5 8 . 23 and f a i l u r e was mainly found i n marketing and management p r a c t i c e s . For example, o v e r - e x t e n s i o n of p l a n t and equip-ment was a freq u e n t causs o f f a i l u r e . Another study to determine the causes of f a i l u r e of smal l manufacturing f i r m s found t h a t u n s u c c e s s f u l companies had p o o r l y informed managements whose d e c i s i o n making was based on h i s t o r i c a l precedent or i n d u s t r y p r a c t i c e . The r e s e a r c h by Fowler and Sandberg confirmed t h a t r e l e v a n t d a t a i s u s u a l l y not c o l l e c t e d and when i t i s c o l l e c t e d the i n f o r m a t i o n i s not p r o p e r l y used because the b a s i c nature of d e c i s i o n making, t h a t i s , s e l e c t i n g a l t e r n a t i v e s w i t h r e s p e c t to go a l s and 19 c o n s t r a i n t s , i s not understood. 7 A survey o f small compan-i e s i n Ohio w i t h l e s s than f i v e hundred employees i n d i c a t e d t h a t even some of the most b a s i c tenents of management are 20 not f o l l o w e d i n smal l b u s i n e s s e s . O r g a n i z a t i o n s t r u c t u r e and communications are not w e l l e s t a b l i s h e d . Of more importance from the OR standpoint, o b j e c t i v e s are i l l -•^A.M. Woodhuff, and T.G. Alexander, Success and  F a i l u r e i n Small Manufacturing, ( 1 9 5 8 ) . "^F.P. Fowler and E0W. Sandberg, The R e l a t i o n s h i p  of Management Decision-Making to Small Business Growth, (1964) , 2 0H.F. P u f f , "Problems and P r a c t i c e s of the Small Manufacturer," ( 1 9 6 2 ) , pp. 32 -34 24 d e f i n e d and d e c i s i o n s are made without e x p l i c i t attempts to o b t a i n the r e l e v a n t a v a i l a b l e i n f o r m a t i o n . A l l of these s t u d i e s demonstrate t h a t there i s a need f o r improved manage-ment of s m a l l businesses e s p e c i a l l y w i t h r e s p e c t to a n a l y s i s of i n f o r m a t i o n f o r d e c i s i o n making. A r e c e n t s t a t i s t i c a l study shows t h a t the p r o f i t a b i l i t y o f small United S t a t e s f i r m s , e s p e c i a l l y those w i t h a s s e t s of l e s s than $ 5 0 , 0 0 0 i s s i g n i f i c a n t l y lower than l a r g e r 2 1 companies. The s t a t i s t i c a l a n a l y s i s of company p r o f i t s as a f u n c t i o n of company s i z e as measured by t o t a l a s s e t s i s based i n U.S. Department of I n t e r n a l Revenue d a t a f o r 1 9 5 5 , to 1 9 5 7 • As an example, the a n a l y s i s shows t h a t the average r a t e of r e t u r n on a s s e t s f o r f i r m s w i t h a s s e t s between $50,000 and $ 1 0 0 , 0 0 0 i s 5 . 3 ^ as compared to the h i g h e s t r a t e of r e t u r n , 7 A % f o r the $ 1 0 , 0 0 0 , 0 0 0 to $ 2 5 , 0 0 0 , 0 0 0 s i z e category, and to an approximate 6.Q% average r e t u r n f o r a l l s i z e c a t e g o r i e s . In c o n t r a s t to t h i s r e s u l t are d a t a from Canadian t a x a t i o n s t a t i s t i c s f o r the years of 1 9 5 7 to i 9 6 0 which i n d i c a t e t h a t s m a l l f i r m s i n Canada are j u s t as p r o f i t a b l e as 2 2 l a r g e f i r m s . i n p a r t i c u l a r the average p r e - t a x earnings of f i r m s w i t h a s s e t s of under $100,000 was 2k% as compared to 19% X H . 0 . S t e k l e r , " P r o f i t a b i l i t y and S i z e of Firm", ( 1 9 6 3 ) ^ ^ 1 9 6 4 — R e p o r t of the Royal Commission on Banking and  Finance, ( 1 9 6 4 ) , p. 4 4 . 25 f o r companies w i t h a s s e t s of l e s s than $1,000,000. These f i g u r e s may be d i s t o r t e d by the lower s a l a r i e s of owner managers of s m a l l f i r m s but they i n d i c a t e t h a t small f i r m s are p r o f i t a b l e . Having e s t a b l i s h e d t h a t there i s evidence t h a t g e n e r a l l y s m a l l businesses r e q u i r e improved management, i t can not be s t a t e d t h a t o p e r a t i o n s r e s e a r c h i s a l s o r e q u i r e d . OR i s o n l y one of a l a r g e number of management t o o l s which may improve the o p e r a t i o n s of s m a l l b u s i n e s s e s , others being, improved i n f o r m a t i o n systems p o s s i b l y u s i n g EDP, i n d u s t r i a l e n g i n e e r i n g , market r e s e a r c h and o t h e r s . Indeed, i t may be t h a t the c o s t s of u s i n g o p e r a t i o n s r e s e a r c h exceed the b e n e f i t s which can be d e r i v e d . However, there remains the p o s s i b i l i t y t h a t i n c e r t a i n s i t u a t i o n s , e s p e c i a l l y f o r a n a l y s i s of informa-t i o n f o r r a t i o n a l decision-making, o p e r a t i o n s r e s e a r c h can p r o v i d e s u b s t a n t i a l net b e n e f i t s which w i l l improve the v i a b i l i t y and growth of s m a l l b u s i n e s s e s . In p a r t i c u l a r , o p e r a t i o n s r e s e a r c h can improve equipment a l l o c a t i o n and usage, i n v e n t o r y c o n t r o l , l o c a t i o n s e l e c t i o n , a l l of which have been mentioned as causes of s m a l l business f a i l u r e s . The remainder of t h i s paper i s an attempt to g e n e r a l i z e as to what extent t h i s i s t r u e . CHAPTER I I I THE USE OF OPERATIONS RESEARCH IN SMALL BUSINESSES INCLUDING A SURVEY OF LOCAL EXPERIENCE T h i s chapter aims at answering the f o l l o w i n g q u e s t i o n s : 1) To what extent and w i t h what success i s o p e r a t i o n s r e s e a r c h used i n s m a l l b u s i n e s s e s ? 2) For what reasons i s o p e r a t i o n s r e s e a r c h not used more e x t e n s i v e l y i n s m a l l b u s i n e s s e s ? 3) What are some of the common problems f a c e d by small business managers t h a t might be e f f e c t i v e l y s o l v e d by OR? A s e c t i o n of t h i s chapter i s devoted to each of these q u e s t i o n s i n t u r n . The i n f o r m a t i o n was mainly gleaned from a survey of l o c a l s m a l l business managers; a d e s c r i p t i o n of t h i s survey i s the s u b j e c t o f the f i r s t s e c t i o n . In a d d i t i o n to the l o c a l survey, i n f o r m a t i o n was obtained by i n t e r v i e w i n g l o c a l c o n s u l t a n t s , computer s e r v i c e bureaus and the S e a t t l e o f f i c e of the U.S. Small Business A d m i n i s t r a t i o n . The l i t e r a t u r e was surveyed f o r r e p o r t s of the use of OR i n s m a l l businesses, to support the author's assessment of l o c a l experience. In t h i s r e g ard the U.S. Small Business A d m i n i s t r a t i o n has p u b l i s h e d r e p o r t s of r e s e a r c h on the a p p l i c a t i o n of OR to s m a l l businesses but they do not r e p o r t any a c t u a l usage, and d i s c u s s the problems of u s i n g OR i n s m a l l businesses to a v e r y l i m i t e d extent. 2$ Some of the r e s u l t s of these r e s e a r c h s t u d i e s w i l l be mentioned but i t i s not the purpose of t h i s study to assess t h e i r f i n d i n g s . I. THE SURVEY OF LOCAL SMALL BUSINESSES The c o n s t r a i n t s of time and r e s o u r c e s l i m i t e d the extent of t h i s survey. I d e a l l y a random sample of a p o p u l a t i o n which c o u l d be s p e c i f i c a l l y i d e n t i f i e d would be s e l e c t e d as a b a s i s f o r d e t e r m i n i n g the extent to which o p e r a t i o n s r e s e a r c h i s used. Hoitfever, i t was n e i t h e r p o s s i b l e to i d e n t i f y from r e a d i l y a v a i l a b l e d a t a a l l l o c a l f i r m s w i t h a value added of l e s s than f i v e m i l l i o n nor would I t have been p o s s i b l e to i n t e r v i e w the managers of a l l companies i n a s i g n i f i c a n t random sample. The I n t e r v i e w technique r a t h e r than a mailed q u e s t i o n n a i r e was deemed necessary because of the l a c k of knowledge of o p e r a t i o n s r e s e a r c h among smal l b u s i n e s s managers. Ther e f o r e a l i m i t e d survey of s u b j e c t i v e l y s e l e c t e d companies was made us i n g the i n t e r v i e w technique. Members of the management of twelve s m a l l b u s i n e s s e s i n B.C. were i n t e r v i e w e d . F i v e companies were s e l e c t e d by t h e i r response to a l e t t e r sent to managers of small companies p a r t i c i -p a t i n g i n a one day seminar on o p e r a t i o n s r e s e a r c h . With the other companies, the author was f a m i l i a r w i t h t h e i r o p e r a t i o n s and c o n s i d e r e d them as r e p r e s e n t a t i v e of l o c a l small b u s i n e s s e s . The r e l e v a n t c h a r a c t e r i s t i c s of each company and the p o s i t i o n of the manager(s) i n t e r v i e w e d i s o u t l i n e d i n Table IV. The managers were questioned a c c o r d i n g to the format g i v e n i n Appendix I. The q u e s t i o n s were formulated to o b t a i n 27 an e s t i m a t i o n of the s i z e of the company and the e d u c a t i o n a l l e v e l of the company's management. Subsequently, the extent of the managers' knowledge of o p e r a t i o n s r e s e a r c h and a few common OR techniques was determined, f o l l o w e d by b r i e f explana-t i o n s by the author so as to f a c i l i t a t e the subsequent d i s c u s s i o n . Any experience by the company i n u s i n g OR was then d i s c u s s e d . On the o t h e r hand, i f OR had not been used, the i n t e r v i e w e r d e l v e d i n t o the reasons f o r non-use. In e i t h e r case, the problems of the s m a l l b u s i n e s s were d i s c u s s e d to i d e n t i f y p o s s i b l e areas f o r OR a p p l i c a t i o n . The remainder of t h i s chapter d e a l s w i t h the r e s u l t s of t h i s survey, which are summarized i n Table V, p l u s i n f o r m a t i o n obtained from o t h e r sources as s t a t e d above. I I . THE EXTENT AND SUCCESS OF USE OF OPERATIONS RESEARCH The survey of l o c a l s m a l l businesses p r o v i d e s evidence t h a t o p e r a t i o n s r e s e a r c h i s used to a r a t h e r l i m i t e d extent by s m a l l b u s i n e s s . Four of the twelve companies i n the survey have used o p e r a t i o n s r e s e a r c h to s o l v e one or two problems. However i n none of the companies i s o p e r a t i o n s r e s e a r c h a g e n e r a l a c t -i v i t y o f the f i r m even though i n every company there e x i s t e d problems to which OR might weikl be a p p l i e d . In two companies c o n s u l t a n t s used i t i n the a r e a of i n v e n t o r y c o n t r o l . A foundry r e p o r t e d u s i n g a s m a l l l i n e a r programme f o r minimizing a l l o y i n p u t c o s t s . Another f i r m r e p o r t e d u s i n g CPM s u c c e s s f u l l y f o r c o n t r a c t maintenance p r o j e c t s . 28 TABLE IV COMPANIES AND MANAGERS REPRESENTED IN THE SURVEY Value F o r m a l l y P o s i t i o n F a m i l i a r i t y Added* i n No. of Educated of wit h Company -Industry M i l l i o n s . Employees .Employees. Manager(s) OR A Me t a l - | 1 m i l l . working ~ 9 0 5 Sales Mgr. G e n e r a l l y B D i s t r i - $ 0 . 7 5 m i l l , but i o n 40 - 1 Gen. Mgr. None C Foundry $ 4 m i l l . 2 6 5 1 2 Gen. Mgr. Some D Meta l - $ 2 m i l l , working 140 4 P l a n t Supt.None Pr o d u c t i o n Some Engineer E Real $ 1 . 5 m i l l . E s t a t e no 2 Sec.-Treas.None Cost Acct. Some F Equip- $ 4 m i l l , ment Mfg.' 1 0 0 6 Mgg. D i r . Chief Eng. None G e n e r a l l y G Wood- $ 2 m i l l , working 1 5 0 -4 7 0 6 Chief Eng. Purch. Agent Some None ..... H. . _ Metal- . $ 0 . 5 0 mill... working 40 . 3. P r e s i d e n t None I Mfg. & $ 5 m i l l . D i s t r i b u -t i o n 3 0 0 -800 8 Gen. Mgr. Warehouse Manager None Some J C o n s t r u c - $ 2 m i l l , t i o n Mtlsv 2 0 0 8 Chief Eng. "Accountant Some None K D i s t r i b u - $ 1 . 5 m i l l , t i o n 1 3 0 4 Gen. Mgr. Sales Mgr. Some Some • : :paintMfg. 0 . 7 5 4 5 - 6 5 2 Mgg.' D i r . G e n e r a l l y ^approximate - estimated by author i n some cases. 29 The surveys r e p o r t e d i n Chapter I I a l s o p r o v i d e d evidence t h a t o p e r a t i o n s r e s e a r c h i s used i n f r e q u e n t l y by/ s m a l l b u s i n e s s . A r e c e n t r e p o r t of a survey on the use of modern management techniques by s m a l l businesses i n the A t l a n t i c p r o v i n c e s of Canada found t h a t many techniques, some of which can be grouped under o p e r a t i o n s r e s e a r c h , are used to a v e r y l i m i t e d extent by the companies i n t h e i r s u r v e y . 1 In a d d i t i o n c o n v e r s a t i o n s w i t h l o c a l c o n s u l t a n t s , d a t a c e n t e r p e r s o n n e l , Dr. R. Johnson of the U n i v e r s i t y of Washington and the personnel of the S e a t t l e o f f i c e of the Small Business A d m i n i s t r a t i o n r e v e a l e d o n l y three other i n s t a n c e s of o p e r a t i o n s r e s e a r c h being used by s m a l l companies. Thus there i s c o n s i d e r a b l e evidence to i n d i c a t e t h a t o p e r a t i o n s r e s e a r c h i s used to o n l y a l i m i t e d extent by s m a l l b u s i n e s s . Most of the companies i n the survey who had used opera-t i o n s r e s e a r c h have found the r e s u l t s u s e f u l . One of the companies u s i n g i n v e n t o r y c o n t r o l models was very p l e a s e d w i t h the r e s u l t i n g c o n t r o l system whereas i n the other company some doubt was expressed concerning the u s e f u l n e s s of the r e s u l t s although i t was admitted t h a t i t was too e a r l y to t e l l . In both cases c o n s u l t a n t s were r e -t a i n e d f o r i n s t a l l i n g the systems. In the l a t t e r case, the i n v e n t o r y c o n s i s t e d of one raw m a t e r i a l of d i f f e r e n t J.C. Lavoie, e t a l . "Management Concepts and Methods i n the Smaller Company", (1966). 30 grades and s i z e s i n which the p r i c e and d e l i v e r y f l u c t u a t e d markedly. Als o orders f o r the company's products were based on c o n t r a c t b i d d i n g so t h a t demand was h i g h l y v o l a t i l e . In such a s i t u a t i o n i t can be a p p r e c i a t e d that c o n t r o l l i n g I n v e n t o r i e s i s an extremely d i f f i c u l t problem and e x t e n s i v e use of judgement must be made even when u s i n g a w e l l formu-l a t e d model. In the former case, company K purchases approximately 8 ,000 items from one manufacturer who maintains f a i r l y c onstant d e l i v e r y times of approximately one month. T h i s i n v e n t o r y c o n t r o l system i s run on a computer once a week f o r updating stocks and f o r o r d e r i n g , and once a month f o r f o r e c a s t i n g and changing r e o r d e r q u a n t i t i e s . The system employs an e x p o n e n t i a l smoothing technique f o r f o r e c a s t i n g s a l e s f o r the succeeding three months. Ordering c o s t s , c a r r y i n g c o s t s , stockout c o s t s and l e a d times are u t i l i z e d f o r c a l c u l a t i n g r e o r d e r p o i n t s and r e o r d e r q u a n t i t i e s . Much of the b e n e f i t of t h i s system i s d e r i v e d from c l e r i c a l e f f i c i e n c y through e l e c t r o n i c d a t a p r o c e s s i n g alone. How-ever, c o n s i d e r a b l e b e n e f i t has r e s u l t e d from the r e d u c t i o n of i n v e n t o r y investment and improved customer s e r v i c e . The company's management s t a t e s that the monthly c o s t of approx-i m a t e l y $ 1 , 0 0 0 i n running t h i s on a computer i s w e l l j u s t i f i e d and they p l a n to c o n t r o l more of t h e i r i n v e n t o r y by t h i s method. 31 T h i s company a l s o uses a smal l s c a l e s i m u l a t i o n to assess the p r o s p e c t s of doing business i n a c e r t a i n area f o r a three to f i v e year p e r i o d . S i n g l e best estimates of o p e r a t i n g parameters and business c o n d i t i o n s are used, c a l c u l a t i o n s are performed on a desk c a l c u l a t o r and the r e s u l t i s a simple yes or no as to whether the company should undertake the p r o j e c t . Company J has used c r i t i c a l path methods on a simple, non-computerized b a s i s f o r s c h e d u l i n g c o n t r a c t maintenance p r o j e c t s . T h i s technique i s used to determine when and how many men and re s o u r c e s are r e q u i r e d to complete a p r o j e c t i n the s p e c i f i e d time. No time-cost t r a d e - o f f s are used as i t i s c o n s i d e r e d t h a t time i s g e n e r a l l y f a r more important. The company i s ve r y p l e a s e d w i t h the r e s u l t s o f u s i n g t h i s OR technique and s t a t e d t h a t without CPM, some p r o j e c t s c o u l d not have been completed i n time. Needless to say, they p l a n to continue I t s use. A survey o f the l i t e r a t u r e r e v e a l e d o n l y two r e p o r t s on the use of OR i n s m a l l business, but i n c l u d e d a f a i r l y 2 d e t a i l e d account of i t s use i n one f i r m . T h i s f i r m s t a r t e d u s i n g OR "by a c c i d e n t " when they obtained the s e r v i c e s o f a mathematician as an a s s i s t a n t bookkeeper and he became i n t e r e s t e d i n a p p l y i n g a q u a n t i t a t i v e approach to the comprehension and c o n t r o l of the company's problems. T h i s company r e p o r t e d u s i n g OR i n ( l ) media s e l e c t i o n and H.L. Baum J r . , "The Use of Operations Research i n a Small Company," (1957), PP. 39-^7 32 budgeting f o r a three year a d v e r t i s i n g campaign; (2) s a l e s f o r e c a s t i n g by r e g r e s s i o n a n a l y s i s and (3) p r o d u c t i o n p l a n n i n g and i n v e n t o r y c o n t r o l . Top management appears v e r y impressed by the b e n e f i t s . F o r e c a s t s f o r f i v e q u a r t e r s are r e p o r t e d to have an e r r o r range of two to f i v e p ercent where p r e v i o u s l y f o r e c a s t s c o u l d be " o f f by as much as twenty or t h i r t y p e r c e n t . " J F i n i s h e d goods i n v e n t o r y are kept at reasonable l e v e l s , the work f o r c e i s more e f f i c i e n t l y employed and storage and p r o d u c t i o n space have been f r e e d f o r new products. Other r e p o r t e d b e n e f i t s o f t h i s more d i s c i p l i n e d approach to business problems are i n c r e a s e d customer g o o d w i l l and b e t t e r o v e r a l l p l a n n i n g . U n f o r t u n a t e l y n e i t h e r the s i z e of the company nor the s i z e o f the OR group are r e p o r t e d but i t i s s t a t e d t h a t the saving i n manpower u t i l i z a t i o n through p r o d u c t i o n p l a n n i n g was s u f -f i c i e n t alone to cover the c o s t of the " s m a l l " OR a c t i v i t y . The other r e p o r t d e s c r i b e s how an o p e r a t i o n s r e s e a r c h study"was formulated and implemented f o r deter m i n i n g the s i z e L and type of hog to buy each day at d i f f e r e n t p r i c e l e v e l s . J I b i d . , p. 44 h, K.S. Axelson, "Examples of Operations Research A p p l i c a t i o n , " ( 1 9 6 2 ) , pp. 7 8 - 7 9 . 33 A n a l y s i s of meat v a l u e s f o r each type and s i z e of hog and o p e r a t i n g c o s t s made i t p o s s i b l e to simulate one day^s o p e r a t i o n s so as to c a l c u l a t e the breakeven p r i c e s f o r each s i z e and type of hog. T h i s d a t a was d i s p l a y e d on a c h a r t so t h a t the hog buyers purchased hogs o n l y i f the market p r i c e was l e s s than the breakeven p r i c e . I I I . REASONS WHY OPERATIONS RESEARCH IS NOT USED EXTENSIVELY IN SMALL BUSINESS The above summaries i n d i c a t e t h a t o p e r a t i o n s r e s e a r c h can be used advantageously i n small b u s i n e s s e s . The r e s u l t s of the survey of l o c a l small businesses and the SBA sponsored r e s e a r c h suggest some reasons why i t i s not used more exten-s i v e l y . The r e s u l t s o f the survey i n t h i s r e g ard are summarized i n Table V. I t Is important to note the r e l a t i o n -s h i p o f these c o n s i d e r a t i o n s f o r each company. For i n s t a n c e , the e x e c u t i v e i n Company H knew no t h i n g about o p e r a t i o n s r e s e a r c h , was not i n t e r e s t e d i n i t and thus he d i d not know which f a c t o r s would hi n d e r h i s company from engaging i n OR. On the other hand, the e x e c u t i v e s of Company F d i s p l a y e d a genuine i n t e r e s t but suggested a number of reasons as to why i t would be d i f f i c u l t to engage i n meaningful o p e r a t i o n s r e s e a r c h . Although these reasons are not n e c e s s a r i l y p e c u l i a r to s m a l l business, they tend to e x i s t more g e n e r a l l y than f o r l a r g e o r g a n i z a t i o n s . The f o l l o w i n g d i s c u s s i o n a l s o i n d i c a t e s why they are more d i f f i c u l t f o r the s m a l l e r f i r m TABLE V SUMMARY OP THE RESULTS OF THE SURVEY Company Had Exposure to OR Top Management F a m i l i a r i t y a C o n s t r a i n t Use OR and p l a n to i n c r e a s e . i t s use A Short Course No No B No D i f f i c u l t to answer No C Not f o r m a l l y Yes Yes D. . Seminar Yes Use but do not p l a n to Increase E ' No " Yes Yes F Yes, but No Not f o r m a l l y No G Yes Seminar P o s s i b l y Wo H No No No I No No No J . Yes Seminar Yes Yes K Yes No Short Course Yes - L • Yes No <3<=> No 3 4 Is i t p o s s i b l e 03 c o u l d a i d management of f i r m ? B e l i e v e i t would not be economical Lack of t r a i n e d p ersonnel i s a c o n s t r a i n t Other c o n s t r a i n t s on use of OR Yes Don't know and not prepared to f i n d out Yes Fear of l o s s of c o n t r o l Yes Probably yes - - - -I t does I t i s economic Yes - -Yes Sometimes i t i s economic Yes F o r e c a s t i n g Yes Not sure Yes — — Yes Don't know Yes F o r e c a s t i n g and i n s u f f i c i e n t d ata D o u b t f u l Probably yes - - D i f f i c u l t y i n f o r e c a s t i n g No Yes — — — _ No Yes - - V/ork not s o p h i s t i -cated enough I t does I t i s economic Yes - -I t does I t i s economic No, Use Finances Consultants Yes Yes Yes I n s u f f i c i e n t Data 35 to overcome. N o n - a n a l y t i c a l Approach to Management. There was some evidence In t h i s survey t h a t managers do not have a f o r m a l i z e d r a t i o n a l approach to d e c i s i o n making. When asked to g i v e examples of problems to which OR might be u s e f u l l y a p p l i e d , the managers mentioned aspects of t h e i r o p e r a t i o n s which reduce company p r o f i t s but o f t e n suggested t h a t n o t h i n g c o u l d be done to improve the s i t u a t i o n because t h e i r "business i s d i f f e r e n t " . Some managers suggested t h a t i f the environment was d i f f e r e n t then the problem would be easy to s o l v e , i m p l y i n g t h a t there i s no way to s o l v e the problem i n the present s i t u a t i o n . Thus f a i r l y important problems were ignored without a thorough a n a l y s i s o f the s i t u a t i o n to i d e n t i f y i t s importance and r e l a t i o n s h i p to o r g a n i z a t i o n a l o b j e c t i v e s , the r e a l c o n s t r a i n t s upon i t s s o l u t i o n , and the course of a c t i o n t h a t w i l l y i e l d the h i g h e s t r e t u r n i n terms of the o b j e c t i v e s . In other words, many d e c i s i o n s are made i n t u i t i v e l y or by h i s t o r i c a l precedence. These f i n d i n g s are confirmed i n a study by Fowler and Sandberg f o r the U.S. Small Business A d m i n i s t r a t i o n on the manner i n which smal l businessmen i n one i n d u s t r y make d e c i s i o n s r e l a t i v e to the g o a l s of growth and 36 v i a b i l i t y . The f o l l o w i n g p o i n t s are made i n t h e i r c o n c l u s i o n s : 1 ) "The ( t y p i c a l s m a l l b u s i n e s s ) a d m i n i s t r a t o r ( i n t h e i r study) s p e c i f i e s g o a l s a f t e r the f a c t as opposed to the g e n e r a l concept of a d m i n i s t r a t i o n which i n s i s t s the g o a l s be s p e c i f i e d "ex ante' ."' 2) "Where o p e r a t i n g d e c i s i o n s are made i n the absence of a set of e x p l i c i t g o a l s , a l t e r n a t i v e s are chosen e i t h e r on the b a s i s of h i s t o r i c a l precedent, t r a d i t i o n , or f o l k l o r e ; or by f o l l o w i n g the l e a d e r . " 3) "Even where o b j e c t i v e s are e x p l i c i t l y s t a t e d , i t i s e v i d e n t t h a t what i n f o r m a t i o n i s a v a i l a b l e i s used i n ex post a n a l y s i s of performance r a t h e r than i n the ex ante e v a l u a t i o n of a l t e r n a t i v e courses of a c t i o n . " 4) " F a i l u r e to a p p r e c i a t e the importance of c o n t r o l i n f o r m a t i o n before the f a c t r e s u l t s i n a s i t u a t i o n where r e l e v a n t d a t a i s n e i t h e r generated nor processed f o r ex ante e v a l u a t i o n of a l t e r n a t i v e s . " 5 ) " I t i s q u i t e obvious that there i s absent from among the f i r m s i n t h i s i n d u s t r y , and probably gen-e r a l l y among 's m a l l ' businesses, an a p p r e c i a t i o n of the b a s i c nature of the a d m i n i s t r a t i v e p r o c e s s : d e c i s i o n making r e l a t i v e to g o a l s and a l t e r n a t i v e s . The i r r a t i o n a l p a t t e r n s of behaviour developed i n the a n a l y s i s undoubtedly r e s u l t more from t h i s d e f i c i e n c y than from any s p e c i f i c area of i n e x p e r t n e s s of the i n d i v i d u a l manager." In the present survey, the evidence of the above c h a r a c t e r i s t i c s of d e c i s i o n making was not as e x t e n s i v e but the degree to which i t e x i s t s i s a c o n s t r a i n t on the use of JE..P... Fowler and.-E.W. Sandberg, The R e l a t i o n s h i p of  Management Decision-Making to Small Business Growth^ ( 1 9 6 4 ) pp. 6 5 - 6 7 . 37 OR. Managers must a p p r e c i a t e the value of r a t i o n a l d e c i s i o n making before they w i l l pay f o r the e f f o r t s of o p e r a t i o n s a n a l y s t s to o b t a i n i n f o r m a t i o n which i s u s e f u l f o r s p e c i -f y i n g c o n s t r a i n t s and weighing a l t e r n a t i v e s . Inherent i n a l l o p e r a t i o n s r e s e a r c h i s r a t i o n a l d e c i s i o n making. Indeed o p e r a t i o n s r e s e a r c h can be regarded as a p p l i e d d e c i s i o n t h e o r y . ^ Conversely, the executive who understands the theory of r a t i o n a l d e c i s i o n making i s more l i k e l y to a p p r e c i a t e the p o s s i b l e b e n e f i t s t h a t can be d e r i v e d from o p e r a t i o n s r e s e a r c h . The obvious s o l u t i o n has to do w i t h e d u c a t i o n a l programmes but i t i s beyond the scope of t h i s paper to d e l v e i n t o t h a t s u b j e c t . Management's Lack of F a m i l i a r i t y w i t h OR Most of the managers i n t e r v i e w e d had some impressions c o n c e r n i n g o p e r a t i o n s r e s e a r c h , or one or more OR techniques, but any knowledge was expressed i n r a t h e r vague terms.v (see Table M)» Almost none of the managers i n t e r v i e w e d had a working knowledge of any of the techniques except of course i n the few i n s t a n c e s where OR was used i n the f i r m and the manager was d i r e c t l y i n v o l v e d . Even the people who had attended the one day seminar on o p e r a t i o n s r e s e a r c h had v e r y u n c e r t a i n knowledge as to the aims, methods and r e s u l t s .... M.K. S t a r r , and D.W. M i l l e r , E x e c u t i v e D e c i s i o n s and  Operations Research, ( i 9 6 0 ) , p. 1 0 3 . 38 of OR. There seems to be no r e l a t i o n s h i p between the number of f o r m a l l y educated employees (and g e n e r a l l y the managers i n t e r v i e w e d were f o r m a l l y educated beyond hi g h s c h o o l ) and the degree of f a m i l i a r i t y w i t h o p e r a t i o n s r e s e a r c h . Operations r e s e a r c h i s a r a t h e r new approach to i n c r e a s i n g b usiness p r o d u c t i v i t y and has been taught o n l y f o r the l a s t few years at most business s c h o o l s . Business p r e s s u r e s u s u a l l y keep the s m a l l business manager too preoccupied to > spend munch time i n v e s t i g a t i n g new a i d s to management. Theref o r e t h i s l a c k of f a m i l i a r i t y i s not s u r p r i s i n g and i s l i k e l y to change very s l o w l y even w i t h the i n c r e a s i n g i n t e r e s t i n management s c i e n c e and business a p p l i c a t i o n s of computers. The obvious s o l u t i o n i s to provide o p p o r t u n i t i e s f o r exposure to the approach of o p e r a t i o n s r e s e a r c h so t h a t managers w i l l be motivated to study the p o s s i b i l i t y of i t s use i n t h e i r o r g a n i z a t i o n s . In t h i s regard, i t i s i n t e r e s t -i n g to note t h a t most of the managers who had some knowledge of OR had obtained i t a t s h o r t courses and seminars and g e n e r a l l y were q u i t e i n t e r e s t e d i n the p o s s i b i l i t y of u s i n g OR. Even they, however, f e l t a need to know more about i t b e f o r e i n i t i a t i n g an OR approach to t h e i r b usiness problems:-, (see Table V.). The managers who were by and l a r g e i g n o r a n t of OR 39 f r e q u e n t l y expressed the d i c t a , " o u r f i r m i s d i f f e r e n t " or "our work i s not s o p h i s t i c a t e d enough f o r the use of these te c h n i q u e s . " T h i s d i s p l a y s a g e n e r a l l a c k o f a p p r e c i a t i o n f o r the aims and techniques of o p e r a t i o n s r e s e a r c h i n t h a t OR attempts to d e a l w i t h the s i t u a t i o n as i t e x i s t s i n any o r g a n i z a t i o n , not wit h some t h e o r e t i c a l model. Thus, although these managers d i d not f e e l t h a t t h e i r l a c k of f a m i l i a r i t y was a c o n s t r a i n t on the use of OR i n t h e i r f i r m s , the author concluded t h a t i n f a c t i t was a r e a l c o n s t r a i n t . Lack of T r a i n e d Personnel Managers i n s i x of the companies i n t e r v i e w e d s t a t e d t h a t the absence i n t h e i r o r g a n i z a t i o n s of people t r a i n e d i n o p e r a t i o n s r e s e a r c h or r e l a t e d d i s c i p l i n e s was a c o n s t r a i n t on t h e i r use of OR. C e r t a i n l y the s t a f f who are to under-take an o p e r a t i o n s r e s e a r c h approach must have some a p p r e c i a t i o n f o r the s c i e n t i f i c method'' i n g e n e r a l and p r e f e r a b l y a working knowledge of the common OR techniques. Although some of the people i n t e r v i e w e d had been to seminars or s h o r t courses on OR, i t was obvious t h a t t h i s had not pro v i d e d them w i t h a working knowledge and g e n e r a l l y i t was these people who expressed the b e l i e f t h a t the l a c k of See Chapter 1, p. 4 40 t r a i n e d personnel i s a c o n s t r a i n t . For the presen t there appears to be a s c a r c i t y of t r a i n e d o p e r a t i o n s a n a l y s t s . Even i f they were a v a i l a b l e many smal l companies f e e l t h a t they c o u l d not p r o v i d e enough c h a l l e n g e or a f f o r d to r e t a i n them on s t a f f . One a l t e r n a t i v e i s f o r the sm a l l company to have t h e i r own people t r a i n e d as i s the case w i t h one of the companies now u s i n g OR. Short courses are o f f e r e d by c o n s u l t a n t s , computer manufacturers and u n i v e r s i t i e s , but other than f o r s p e c i f i c a p p l i c a t i o n s a working knowledge of o p e r a t i o n s r e s e a r c h i s not obtained, e s p e c i a l l y i f the employee does not a l r e a d y have an educa t i o n i n mathematics, e n g i n e e r i n g or s c i e n c e . Of course there i s the p o s s i b i l i t y of u s i n g c o n s u l t a n t s as a s u b s t i t u t e f o r f u l l - t i m e OR a n a l y s t s and t h i s w i l l be d i s c u s s e d i n the f o l l o w i n g chapter. F o r e c a s t i n g Problems The managers of three f i r m s d i s c u s s e d the v e r y r e a l problem of f o r e c a s t i n g f o r the small b u s i n e s s . These managers had a f a i r l y good understanding of OR and f u l l y r e a l i z e d the importance of f o r e c a s t i n g f o r i n v e n t o r y c o n t r o l , s c h e d u l i n g , e t c . For many sm a l l f i r m s , e s p e c i a l l y i n the c a p i t a l equipment i n d u s t r i e s , s a l e s f l u c t u a t e markedly and no doubt such f l u c t u a t i o n s are d i f f i c u l t to p r e d i c t . How-eves a c a r e f u l study of the f a c t o r s which c o n t r o l s a l e s 41 and i n some cases c a r e f u l trend a n a l y s i s may i n c r e a s e f o r e c a s t i n g accuracy as witnessed by the experience of o Company K i n our survey and the Noreen C o r p o r a t i o n , two small companies which use e x p o n e n t i a l smoothing and r e -g r e s s i o n a n a l y s i s r e s p e c t i v e l y f o r s a l e s f o r e c a s t i n g . I f i n v e n t o r i e s are c a r r i e d and i f manufacturing schedules are based on expected s a l e s as w e l l as orders on hand, then by i m p l i c a t i o n some f o r e c a s t i n g i s done. Ther e f o r e attempts to put f o r e c a s t i n g on an e x p l i c i t , r a t i o n a l b a s i s w i l l p r o v i d e a b a s i s f o r b e t t e r p l a n n i n g . However, as compared to l a r g e r companies who e x e r c i s e some c o n t r o l over the market, s a l e s f o r e c a s t i n g i s g e n e r a l l y a more d i f f i c u l t problem f o r small businesses to s o l v e . C o n c u r r e n t l y the net b e n e f i t s from s c i e n t i f i c a l l y based f o r e c a s t s are g e n e r a l l y not as l a r g e , i n t h a t f o r a g i v e n r e l a t i v e improvement ab s o l u t e b e n e f i t s w i l l be l e s s f o r the s m a l l company whereas r e s e a r c h c o s t s may be the same. Thus the d i f f i c u l t y of s a l e s f o r e c a s t i n g as r e q u i r e d f o r op e r a t i o n s r e s e a r c h r e p r e s e n t s a very r e a l problem which cannot be answered except i n the context of the economic assessment of u s i n g OR i n a p a r t i c u l a r s i t u a t i o n . Baum, op_. c i t . , pp. 43-45 42 Data A v a i l a b i l i t y Only two managers expressed the o p i n i o n that s u f f i c i e n t , a c c u r a t e data was probably not a v a i l a b l e f o r meaningful a n a l y s i s , although t h i s i s probably p r e v a l e n t among s m a l l b u s i n e s s e s . T h i s o p i n i o n i s confirmed by Fowler and Sandberg,^ and Holdren et a l 1 ^ based on t h e i r r e s e a r c h . Most sma l l b u s i n e s s e s do not have w e l l e s t a b l i s h e d i n f o r m a t i o n systems which i s not s u r p r i s i n g i f t h e i r management does not use an a n a l y t i c a l approach to d e c i s i o n making. Accurate, meaningful d a t a i s a n e c e s s i t y f o r any o p e r a t i o n s research."'" 1 How e l s e can the o p e r a t i o n s be observed and r e p r e s e n t e d by a model which i s u s e f u l f o r d e s c r i p t i o n and p r e d i c t i o n ? Even i f the company does c o l l e c t and r e c o r d d a t a i t i s o f t e n not u s e f u l f o r o p e r a t i o n s r e s e a r c h as i s noted i n the case study i n Chapter V. Of course, f o r any company i t i s d i f f i c u l t to f o r e t e l l what d a t a i s going to be r e q u i r e d f o r a p a r t i c u l a r OR study. T h i s suggests t h a t OR should be a c o n t i n u i n g a c t i v i t y c o o p e r a t i n g w i t h Fowler and Sandberg, op_. c i t . , pp. 67-68. 1 0B.R. Holdren, e t a l , "Operations Research i n Small B u s i n e s s : A Case Study," (1963), p. 55. 1 1 Axel son, . op_. c i t . , p. 78. 43 the systems a n a l y s i s f u n c t i o n to generate the necessary d a t a and to improve and update OR models. Whether or not t h i s i d e a l s i t u a t i o n can be j u s t i f i e d i n a smal l company can o n l y be answered i n a p a r t i c u l a r case. In g e n e r a l however, the a p p l i c a t i o n of OR i n smal l businesses will be s e r i o u s l y hampered by the l a c k of accur a t e , meaningful d a t a . E l e c t r o n i c Computing A v a i l a b i l i t y None of the managers that were i n t e r v i e w e d suggested t h a t the co s t or a v a i l a b i l i t y of computers was a reason f o r not u s i n g OR i n s p i t e of the f a c t t h a t the l e a s i n g of computers can be q u i t e expensive f o r the small company. A r e c e n t study of Canadian computer users shows t h a t f o r busine s s e s w i t h s a l e s of up to ten m i l l i o n d o l l a r s the mean co s t i s over one per cent of s a l e s and the upper q u a r t i l e i s over two per cent o f sales.12 Thus f o r a f i r m w i t h t en m i l l i o n d o l l a r s i n s a l e s , the c o s t of l e a s i n g and o p e r a t i n g a computer v x i l l l i k e l y be a t l e a s t $100,000 per year and coul d c o n c e i v a b l y be more than $200,000 per year. Even so, two f i r m s s t a t e d t h e i r i n t e n t i o n s to e v e n t u a l l y purchase or l e a s e t h e i r own computers. 12V.W... Ruskin, Computer User F a c t s : 1967/68. (1968), E x h i b i t 6. 44 Not a l l OR models need e l e c t r o n i c computers to process the d a t a i n p u t s and s o l v e f o r the optimum or s a t i s f a c t o r y -s o l u t i o n ; as f o r i n s t a n c e w i t h the l i n e a r program being used by Company C and the CPM used by Company J . However f o r c o n t r o l of l a r g e i n v e n t o r i e s , s o l u t i o n of l a r g e l i n e a r programmes, e t c . there i s no doubt t h a t access to an e l e c -t r o n i c computer i s h i g h l y d e s i r a b l e i f not e s s e n t i a l . The v a r i o u s means by which access to an e l e c t r o n i c computer and r e l a t e d s e r v i c e s can be obtained are d e t a i l e d i n Chapter IV. Operations Research i s Not Economical f o r the Small F i r m In t h a t most of the above problems can be r e s o l v e d by e d u c a t i o n or the a p p l i c a t i o n of money, the r e a l c r i t e r i a i s whether or not the b e n e f i t s from u s i n g OR are g r e a t e r than the c o s t s . The managers of f i v e companies suggested t h a t , based on t h e i r understanding of OR, they doubted t h a t i t would be economical f o r t h e i r b u s i n e s s . U n f o r t u n a t e l y three of these managers had v e r y vague idea s as to what OR i s . Of the other companies i n the survey, three were u s i n g OR w i t h g e n e r a l l y s a t i s f a c t o r y r e s u l t s , two expressed no o p i n i o n on i t s economic f e a s i b i l i t y and two others thought t h a t i t probably was economic but there are other c o n s t r a i n t s on i t s use i n t h e i r companies. (see Table I I I ) . B a s i c a l l y these remarks r e p r e s e n t management a t t i t u d e s r a t h e r than c a r e f u l a n a l y s i s . The o p i n i o n t h a t OR i s f e a s i b l e f o r s m a l l 45 b u s i n e s s i n some s i t u a t i o n s has been expressed by r e s e a r c h e r s who have s t u d i e d the problem f o r the U.S. Small Business 13 14 A d m i n i s t r a t i o n . There are f a c t o r s i n a d d i t i o n to the problems out-l i n e d above which tend to make the use of o p e r a t i o n s r e s e a r c h i n a s m a l l b u s i n e s s l e s s p r o f i t a b l e than f o r l a r g e o r g a n i z a -t i o n s . F r e q u e n t l y problems of s m a l l businesses are j u s t as complex to s o l v e as the l a r g e company's problems i f c a r r i e d to the same degree of refinement. For i n s t a n c e , the problem of managing i n v e n t o r i e s of ten thousand items i s not more complex f o r the company whose d o l l a r volume turnover i s ten times t h a t of the other company's, and y e t the p o t e n t i a l d o l l a r savings would g e n e r a l l y be much g r e a t e r f o r the f i r s t company. In o t h e r cases, the complexity of problem i s much l e s s f o r the s m a l l company. By example, the problem of s c h e d u l i n g i n a company performing j u s t one or two o p e r a t i o n s on s i m i l a r p a r t s i s e a s i e r to d e a l w i t h than s c h e d u l i n g i n a company which b u i l d s complex machines by performing many s e q u e n t i a l o p e r a t i o n s on a wide v a r i e t y of p a r t s , and most l i k e l y the second f i r m i s l a r g e r than the f i r s t . In any case, whether the c o s t of f o r m u l a t i n g and implementing d e c i s i o n r u l e s based on o p e r a t i o n s r e s e a r c h i s the same or l e s s f o r the s m a l l company, the p o t e n t i a l b e n e f i t s are almost c e r t a i n l y l e s s •^Holdren et a l , l o c . c i t . n L W.J. Gavett and J.M. A l l d e r i d g e , Operations A n a l y s i s i n Small Manufacturing Firms. (196*31 4 6 f o r s i m i l a r types of problems. Other f a c t o r s o p e r a t i n g a g a i n s t the economic a p p l i c a t i o n of OR i n small businesses are h i g h e r i n c r e m e n t a l c o s t of OR e x p e r t i s e and e l e c t r o n i c computing c a p a c i t y . However, these w i l l be d i s c u s s e d i n the ensuing chapter. IV. SMALL BUSINESS PROBLEMS FOR OR The range of problems experienced by s m a l l businesses i n attempting to remain v i a b l e and p r o f i t a b l e and h o p e f u l l y to expand are no doubt c o n s i d e r a b l e ; but not a l l such problems are s u i t a b l e f o r o p e r a t i o n s r e s e a r c h . The formu-l a t i o n of the q u e s t i o n n a i r e was an attempt to a c q u i r e some i n s i g h t i n t o p o s s i b l e areas i n which OR might u s e f u l l y be a p p l i e d . The r e s u l t s i n t h i s r e g a r d were d i s a p p o i n t i n g . No doubt the q u e s t i o n s could have been formulated f o r more e f f e c t . A l s o the e x p r e s s i o n of the managers was c o n s t r a i n e d by t h e i r l i m i t e d knoxtfledge of OR. A t h i r d reason f o r the survey's f a i l u r e to p o r t r a y a wide v a r i e t y of p o s s i b l y i n t e r e s t i n g s u b j e c t s f o r o p e r a t i o n s r e s e a r c h was t h a t a c e r t a i n s t a t e of a f f a i r s i s o n l y regarded as a problem i f i t i s brought to the a t t e n t i o n of the manager as such. For i n s t a n c e , the head melter i n a foundry i s r e s p o n s i b l e f o r s p e c i f y i n g the source m a t e r i a l s f o r each a l l o y and u s u a l l y t h i s w i l l be based on h i s t o r i c a l precedence or a salesman's i n f l u e n c e . Determining the a p p r o p r i a t e mix i s not a problem 47 f o r the melter or top management because no one has drawn t h e i r a t t e n t i o n to p o t e n t i a l savings i n o p e r a t i n g at the optimum. In s p i t e of these c o n s i d e r a t i o n s , p r o d u c t i o n s c h e d u l i n g and i n v e n t o r y c o n t r o l were f r e q u e n t l y mentioned as p o s s i b l e problem areas to which OR might be a p p l i e d . Also some managers expressed a d e s i r e to formulate a more comprehensive method f o r making c a p i t a l expenditure d e c i s i o n s . These managers f e l t t h a t too many f a c t o r s were being overlooked i n d e c i d i n g between a m u l t i t u d e of a l t e r n a -t i v e s . The s t u d i e s conducted under the auspices of the U.S. Small Business A d m i n i s t r a t i o n have p o i n t e d out other problem areas to which OR might be advantageously a p p l i e d i n small b u s i n e s s e s . The e n t i r e f i e l d of marketing s t r a t e g y i s suggested .--^  equipment replacement, equipment a l l o c a t i o n - ^ and job shop e s t i m a t i n g 1 ^ models have a l s o been formulated f o r use by s m a l l companies. As to whether the a p p l i c a t i o n of OR to these problems r e s u l t s i n a net b e n e f i t f o r s m a l l businesses can o n l y be -^Holdren et a l , op_. c i t . , pp. 25-27. l 6 I b i d . , pp. 27-52. -^Gavett and A l l d e r i d g e , op_. c i t . p. 5. determined i n a p a r t i c u l a r case. Nor i s i t the purpose of t h i s paper to assess i n g e n e r a l terms the m e r i t s and d e f i c i e n c i e s of a p p l y i n g OR i n each of the above areas. Rather, i n the two succeeding chapters a more d e t a i l e d examination w i l l be made of the reasons g i v e n above as to why OR i s not used i n s m a l l b u s i n e s s . In p a r t i c u l a r , Chapter IV w i l l attempt to answer the q u e s t i o n s : Can the use of c o n s u l t a n t s r e s o l v e the smal l company's d e f i c i e n c y i n o p e r a t i o n s a n a l y s t s ? What computer f a c i l i t i e s are econ o m i c a l l y a v a i l a b l e f o r implementing OR i n small b u s i n e s s e s ? Chapter V i s the r e p o r t of a case study on the prospects o f a p p l y i n g o p e r a t i o n s r e s e a r c h i n a p a r t i c -u l a r company, i n c l u d i n g an assessment of d a t a d e f i c i e n c i e s , s a l e s f o r e c a s t i n g d i f f i c u l t y , and the economic f e a s i b i l i t y of a p p l y i n g OR i n the area of i n v e n t o r y management. CHAPTER IV CONSULTANTS AND COMPUTERS The preceding d i s c u s s i o n has i d e n t i f i e d the l a c k o f t r a i n e d personnel and the c o s t of e l e c t r o n i c computers as two reasons why OR i s not being used i n small b u s i n e s s e s . The f i r s t p a r t of the present chapter i s an assessment of the extent to which s m a l l b u s i n e s s e s can r e l y on o u t s i d e c o n s u l t a n t s as s u b s t i t u t e s f o r s t a f f OR a n a l y s t s . An examination of the b e n e f i t s o f u s i n g c o n s u l t a n t s and the f a c t o r s g i v i n g r i s e to the r e l a t i v e l y high c o s t of t h e i r s e r v i c e s w i l l l e a d to some recommendations f o r t h e i r e f f e c t i v e r e t e n t i o n by s m a l l b u s i n e s s e s . T h i s s e c t i o n i s mainly based on d i s c u s s i o n s with l o c a l . c o n s u l t a n t s and smal l business managers, e s p e c i a l l y those who had used c o n s u l t a n t s . The subsequent p a r t of t h i s chapter w i l l examine the advantages and c o s t s of computer s e r v i c e bureaus, computer ti m e - s h a r i n g and smal l computers as means by which sma l l b u s i n e s s e s can o b t a i n the e l e c t r o n i c computing c a p a c i t y t h a t i s o f t e n necessary f o r f o r m u l a t i n g and implementing OR s o l u t i o n s to smal l business problems. In t h i s regard, the author had d i s c u s s i o n s w i t h d a t a centre managers, r e p r e s e n t a t i v e s o f computer manufacturers, and computer c o n s u l t a n t s . I. OR CONSULTANTS FOR SMALL BUSINESSES 50 Most management c o n s u l t a n t s have o p e r a t i o n s r e s e a r c h e r s on t h e i r s t a f f . Some computer s e r v i c e c e n t r e s a l s o have q u a l i f i e d o p e r a t i o n s a n a l y s t s who are r e a d i l y a v a i l a b l e . For the smal l business there are some r a t h e r obvious advan-tages i n r e t a i n i n g the s e r v i c e s of an OR c o n s u l t a n t f o r an o p e r a t i o n s study. Most c o n s u l t a n t s have a wide p r a c t i c a l experience backed by a knowledge of the t h e o r e t i c a l a s p e c t s . T h i s , w i t h t h e i r a n a l y t i c a l approach to business problems, permits c o n s u l t a n t s to come q u i c k l y to the essence of the problem and to a p r a c t i c a l approach to i t s s o l u t i o n . A d d i t i o n a l l y , the c o n s u l t a n t can i d e n t i f y other aspects of the o p e r a t i o n which can be more e f f e c t i v e l y c o n t r o l l e d by implementing OR formulated d e c i s i o n r u l e s . C o n sultants can a l s o t r a i n company personnel f o r implementing the r e s u l t s of an OR study and p o s s i b l y to a degree s u f f i c i e n t f o r doing t h e i r own a n a l y s i s i n s p e c i f i c areas. For i n s t a n c e , the c o n s u l t a n t might t r a i n the p r o d u c t i o n manager i n the use of l i n e a r d e c i s i o n r u l e s f o r p r o d u c t i o n s c h e d u l i n g . These advantages are i n a d d i t i o n to the f a c t t h a t r e t a i n -i n g an OR c o n s u l t a n t enables the smal l business to engage i n e f f e c t i v e o p e r a t i o n s r e s e a r c h without having to employ a f u l l - t i m e s p e c i a l i s t which may be f a i r l y c o s t l y , e s p e c i a l l y i f there i s I n s u f f i c i e n t OR work and the person 51 i s not e f f e c t i v e i n other areas of the organization. On the other hand, the services of a consultant are r e l a t i v e l y expensive f o r the small business. For instance, i t has been suggested by consultants that the formulation and implementation by a consultant of an operations research technique i n a major business function, such as inventory control or scheduling, would cost at least $20,000 and for most small businesses t h i s corresponds to a major c a p i t a l expenditure. The basic reasons f o r the high cost are (1) the r e l a t i v e l y high fees of consultants as compared to salaried employees, (2) the time i t takes the consultant to under-stand the organization and operation of the p a r t i c u l a r company and (3) the time required to assess available data and estimate operating parameters from i t . Consultants obtain f a i r l y high s a l a r i e s as a r e s u l t of t h e i r q u a l i f i c a t i o n s but a greater contributing factor to high fees i s the r e l a t i v e l y high overhead of consulting firms mainly due to the need to have s u f f i c i e n t personnel to handle assignments whenever they may develop. In other words, the firm has to bear the expense of inactive con-sultants so as to be able to service c l i e n t s immediately upon request. A Harvard University study has found, i n surveying small businesses as to t h e i r use of consultants, that eighty-seven per cent of the non-users regarded consultants' fees as a s i g n i f i c a n t concern to them while 52 only twenty-four per cent of the users stated that cost was an important consideration. 1 Consequently the Harvard study recommends that consultants to small businesses keep t h e i r overhead low, t h e i r operations small and f l e x i b l e , and spread t h e i r charges over a r e l a t i v e l y long period. Obviously, one means to create f l e x i b i l i t y and reduce overhead i s for the consulting firm to employ q u a l i f i e d personnel i n periods of peak a c t i v i t y , that i s , on a part-time basis. Every business i s d i f f e r e n t i n the detailed aspects of i t s operations and the consultant must completely under-stand not only the p a r t i c u l a r phase of the operation which presents the problem but also i t s interaction with other aspects of the operation. Therefore, a considerable amount of the consultant's time i n each assignment i s spent learn-ing about the operation. For instance, he must understand the objectives and operating environment of the organization, the functional areas of authority and the constraints on decision a l t e r n a t i v e s . Furthermore, t h i s task i s greatly complicated i f the consultant has no previous experience i n the p a r t i c u l a r industry. One means by which t h i s H.C. Krentzman, and J.N. Samaris, "Can Small Businesses Use Consultants?" (I960) p. 130. 53 s i t u a t i o n can be r e l i e v e d i s f o r the s m a l l f i r m to maintain a c o n t i n u i n g r e l a t i o n s h i p w i t h one c o n s u l t a n t who t h e r e f o r e must be a b l e to g i v e a s s i s t a n c e i n many other f u n c t i o n s of the o r g a n i z a t i o n . That i s , the c o n s u l t a n t should have not o n l y a good working knowledge of OR but a l s o of o r g a n i z a t i o n theory, marketing, f i n a n c e , e t c . i n order to f a c i l i t a t e t h i s c o n t i n u i n g r e l a t i o n s h i p . U n f o r t u n a t e l y , most s m a l l businesses do not have r e a d i l y a v a i l a b l e the d a t a ivhich i s necessary to formulate models of d e c i s i o n s i t u a t i o n s . Of course, t h i s i s a l s o a problem i n l a r g e companies but i t a p p a r e n t l y e x i s t s to a g r e a t e r extent 2 i n s m a l l f i r m s . For t h i s reason the c o n s u l t a n t spends c o n s i d e r a b l e time determining the accuracy and r e l e v a n c e of a v a i l a b l e data, and e s t i m a t i n g o p e r a t i n g parameters which are not e x p l i c i t l y a v a i l a b l e from the f i r m s i n f o r m a t i o n system. In t h i s r e g a r d the s m a l l b u s i n e s s can f a c i l i t a t e o p e r a t i o n s a n a l y s i s by upgrading i t s i n f o r m a t i o n system, perhaps w i t h the a d v i c e of the OR c o n s u l t a n t who i s b e t t e r q u a l i f i e d to p r e d i c t the i n f o r m a t i o n requirements. In a d d i t i o n to the h i g h c o s t of r e t a i n i n g c o n s u l t a n t s , the s m a l l business must expend a c o n s i d e r a b l e amount of employee and e x e c u t i v e time i n working w i t h the c o n s u l t a n t , ^See Chapter V; a l s o Fowler and Sandberg, The R e l a t i o n -s h i p of Management Decision-Making to Small Business Growth. 1964. 54 e s p e c i a l l y i n g i v i n g him a complete understanding of the f i r m ' s business and o p e r a t i o n s . T h i s can be a r e l a t i v e l y l a r g e expense i n t h a t the s m a l l company r e l i e s on fewer key personnel to c o n t r o l i t s o p e r a t i o n s , and consequently they are v e r y busy. The t o t a l time t h a t the managers are r e q u i r e d can be reduced by the company m a i n t a i n i n g a c o n t i n u i n g r e l a t i o n s h i p w i t h the c o n s u l t a n t and by the c o n s u l t a n t ' s w i l l i n g n e s s to go i n t o 'the shop* to see f o r h i m s e l f how the business i s run. Another c o s t of employing c o n s u l t a n t s , which may or may not be r e a l , but i s o f t e n mentioned by s m a l l business e x e c u t i v e s , i s the exposure of 'company s e c r e t s ' to o u t s i d e people. G e n e r a l l y , most s m a l l businesses don't have as many s e c r e t s as they may t h i n k . Also the c o n s u l t a n t cannot e t h i c a l l y inform o t h e r s of s p e c i a l aspects of a client's o p e r a t i o n s . S t i l l he may g a i n 'experience' from the company's o p e r a t i o n and see where a c e r t a i n procedure might be u s e f u l i n another c l i e n t ' s o p e r a t i o n . On the whole, t h i s c o s t i s probably g r e a t l y overemphasized and on the o t h e r hand, i f a f i r m i s so f a r ahead" i l l its f i e l d , , i t probably doesn't need c o n s u l t a n t s . Krentzman and Samaris, op_. c i t . , pp. 135.136 55 In the balance then, although a c o n s u l t a n t ' s s e r v i c e s are expensive, t h e i r employment i s o f t e n the o n l y means o f a p p l y i n g OE and thus the a p p l i c a t i o n of o p e r a t i o n s r e s e a r c h i s r e l a t i v e l y expensive f o r the s m a l l b u s i n e s s . T h i s can be reduced by a c o n t i n u i n g r e l a t i o n s h i p w i t h the c o n s u l t a n t p a r t i c u l a r l y i f he can a s s i s t i n other areas; by the develop-ment of meaningful i n f o r m a t i o n systems; and by having the c o n s u l t a n t t r a i n the f i r m ' s personnel In the r e l e v a n t aspects of o p e r a t i o n s r e s e a r c h . I I . COMPUTER SERVICES FOR SMALL BUSINESSES E l e c t r o n i c computing c a p a c i t y i s f r e q u e n t l y a p r e -r e q u i s i t e to the f o r m u l a t i o n and implementation of o p e r a t i o n s r e s e a r c h as i n d i c a t e d i n Chapter I I I . To own or l e a s e e l e c t r o n i c computers has In the past been p r o h i b i t i v e f o r s m a l l b u s i n e s s e s . Even wi t h the marked r e d u c t i o n of computer c o s t s , medium and l a r g e s i z e computers are beyond the means of the t y p i c a l s m a l l company. However, computer s e r v i c e bureaus, computer t i m e - s h a r i n g and s m a l l computers wi t h l i m i t e d c a p a c i t y are a l t e r n a t i v e means of e c o n o m i c a l l y o b t a i n i n g computer s e r v i c e s . T h i s s e c t i o n d e a l s w i t h the advantages and disadvantages of each from the p o i n t of view of o b t a i n i n g the e l e c t r o n i c computing c a p a c i t y which o f t e n i s necessary f o r o p e r a t i o n s r e s e a r c h . 56 Computer S e r v i c e Bureaus Computer s e r v i c e bureaus are independent companies or r e g i o n a l o f f i c e s of computer manufacturers who s e l l time, u s u a l l y f o r batch processing,.on medium to l a r g e s i z e computers. In t h a t l a r g e computers can process d a t a more cheaply than s m a l l computers, the c a p a b i l i t y of doing f a i r l y l a r g e l i n e a r programmes, i n v e n t o r y c o n t r o l r o u t i n e s , s i m u l a t i o n s , and other OR techniques i s p r o v i d e d at reasonable c o s t . For i n s t a n c e , a l i n e a r programme which was run f o r about f o r t y hours on a s m a l l computer and never completed, was run and completed i n seven minutes on a l a r g e computer. The computer c e n t r e s g e n e r a l l y s e l l two types of s e r v i c e s . One i s the "block time" r e n t a l of t h e i r computers i n which the c l i e n t b r i n g s h i s own programmes and d a t a i n machine language, and operates the computer. N a t u r a l l y the s e r v i c e bureau takes no r e s p o n s i b i l i t y f o r e r r o r s i n programmes or d a ta. Charges f o r t h i s s e r v i c e v a r y from |100 per hour to | l , 2 0 0 per hour or more depending on the s i z e of the computer. The other type of s e r v i c e i s an undertaking by the bureau to do the complete job from a n a l y s i s of the r e q u i r e -ments, and programming, to p u t t i n g the d a t a i n machine language and p r o c e s s i n g i t , . u s u a l l y on a p e r i o d i c b a s i s . The c o s t of I . J . S e l i g s o n , "Using Computer S e r v i c e s i n Small B u s i n e s s , " (1962), p. 83 57 m a i n t a i n i n g key punch machines and a n c i l l a r y d e v i c e s , programmers and computer o p e r a t o r s i n a d d i t i o n to the hi g h c o s t of i n s t a l l a t i o n and l e a s i n g of the computer i s thus shared by many users, the c l i e n t s of the s e r v i c e bureau. The author was not ab l e to d i s c o v e r any examples of an o p e r a t i o n s r e s e a r c h type problem being processed on a p e r i o d i c b a s i s u s i n g t h i s s e r v i c e of computer c e n t r e s . However, an i n v e n t o r y i n f o r m a t i o n programme which g i v e s item usage, stock r e c e i p t s , s t o c k l e v e l , c o s t of items, e t c . , f o r 1 2 , 0 0 0 items i s processed weekly f o r approximately | 2 , 5 0 0 per year. T h i s charge does not Include the p r e p a r a -t i o n of the d a t a f o r computer i n p u t as the d a t a i s r e c e i v e d as punched paper tape from the t e l e x t e r m i n a l . A l s o the programming c o s t s are not i n c l u d e d . I t does however i n d i c a t e t h a t the s e r v i c e s of a computer c e n t r e are q u i t e reasonable f o r the s m a l l business which r e q u i r e s the batch p r o c e s s i n g of one or two jobs on a p e r i o d i c b a s i s . With batch p r o c e s s i n g there i s some i n e f f i c i e n c y i n having to f e e d the programme and a c e r t a i n p r o p o r t i o n of f i x e d and o l d d a t a i n t o the computer w i t h each run as compared to keeping the d a t a base and programme o n - l i n e . ^ %.R. Brown, "Cost and Advantages of On-Line DP," ( 1 9 6 8 ) , pp. 40-43. 58 G e n e r a l l y , r e t a i n i n g the d a t a base and programmes o n - l i n e i s p o s s i b l e o n l y w i t h c a p t i v e computers or l a r g e independent computers, and i s f e a s i b l e from a b e n e f i t - c o s t p o i n t of view, o n l y i f i t can be accessed randomly and d i r e c t l y by the people who r e q u i r e the i n f o r m a t i o n . T h i s s e r v i c e which i s not p r o v i d e d by most computer c e n t r e s i s c a l l e d t i m e - s h a r i n g and w i l l be d i s c u s s e d subsequently. Although computer s e r v i c e c e n t r e s make a v a i l a b l e the t a l e n t s of programmers and systems a n a l y s t s , they g e n e r a l l y do not have competent o p e r a t i o n s a n a l y s t s f o r f o r m u l a t i n g OR s o l u t i o n s to business problems.^ Nor i s the a v a i l a b i l i t y of canned programmes of OR techniques an a l t e r n a t i v e i n t h a t they must be t a i l o r e d to the p a r t i c u l a r s i t u a t i o n and the i n t e r p r e t a t i o n of the computer p r i n t - o u t r e q u i r e s a degree of f a m i l i a r i t y w i t h the technique. Also the s e r v i c e c e n t r e i s not u s u a l l y w i l l i n g to get i n v o l v e d w i t h the implementa-t i o n of the r e s u l t s . For these reasons, computer s e r v i c e bureaus do not undertake o p e r a t i o n s r e s e a r c h p r o j e c t s although they w i l l r e n t 'block time* on t h e i r computers - and p r o v i d e programming and key punch s e r v i c e s . hi E.J. Watson, "Computer S e r v i c e s f o r Small B u s i n e s s , " (1965), P. 13 5 9 Computer Time-Sharing Time-sharing i s the a b i l i t y of s e v e r a l users to g a i n access to a computer's memory and l o g i c c a p a b i l i t y at more or l e s s the same time. The p r o s p e c t - o f simultaneous access of remote o n - l i n e customers to a c e n t r a l computer has 7 e l i c i t e d the concept of a computer u t i l i t y . T h i s s e r v i c e i s of c o n s i d e r a b l e i n t e r e s t to the small businessman because i t makes some of the c a p a b i l i t i e s of l a r g e e l e c t r o n i c computers a v a i l a b l e to h i s o r g a n i z a t i o n a t any time of the day (or a t l e a s t a t any time when the t i m e - s h a r i n g system i s o n - l i n e ) and at reasonable c o s t . The e s s e n t i a l components of a t i m e - s h a r i n g system a r e : a l a r g e c e n t r a l computer w i t h secondary o n - l i n e memory d e v i c e s such as d i s c , drum or da t a c e l l u n i t s , software packages, t e r m i n a l equipment and communication l i n e s between the t e r m i n a l equipment and the c e n t r a l p r o c e s s o r . Two such systems are a v a i l a b l e l o c a l l y , the RAX system provided by IBM and the Canadian General E l e c t r i c t i m e - s h a r i n g system. Comparative user r a t e s are l i s t e d i n Table VI. T y p i c a l charges f o r oth e r systems are # 3 5 0 per month p r o v i d i n g 5 0 'M.R. Irwin, "Small Business and Time-shared Computers," ( 1 9 6 7 ) , p. 2 1 . 60 8 hours of t e r m i n a l time. These c o s t s w i l l however, vary-s u b s t a n t i a l l y w i t h the d i s t a n c e between the t e r m i n a l and the computer. The managers of a t i m e - s h a r i n g s e r v i c e i n Boston, U.S.A. s t a t e t h a t t h e i r market i s l i m i t e d to a r a d i u s of s i x t y to seventy m i l e s by the c o s t of communication l i n e s . ' In f a c t , with the c o n t i n u i n g r e d u c t i o n of d a t a p r o c e s s i n g c o s t s , communication c o s t s w i l l become the l i m i t i n g f a c t o r of the t i m e - s h a r i n g p o t e n t i a l e s p e c i a l l y i n remote areas. However, there i s some i n d i c a t i o n t h a t improved technology f o r t r a n s m i t t i n g d a t a w i l l s i g n i f i c a n t l y reduce communications c o s t s a l s o . Another user advantage i s the r e l a t i v e ease of u s i n g the system. The s u b s c r i b e r need not have e x t e n s i v e program-ming a b i l i t y and input can be through a normal t e l e t y p e c o n s o l e . For i n s t a n c e many of the Canadian General E l e c t r i c system's programmes are i n the Basi c language which can be l e a r n e d i n one day and the t e r m i n a l i s a standard t e l e x t e l e t y p e w r i t e r . A l s o , the s u b s c r i b e r has access to o n - l i n e programmes which cover a wide v a r i e t y of a p p l i c a t i o n s and i n c l u d e s m a l l l i n e a r programmes, i n v e n t o r y c o n t r o l r o u t i n e s u s i n g economic order q u a n t i t i e s , c a p i t a l investment a n a l y s i s i b i d , p.. 23. I b i d , p. 2k. 6 1 u s i n g Monte C a r l o s i m u l a t i o n s , as w e l l as o t h e r OE techniques. These programmes are e x c e l l e n t f o r s o l v i n g s m a l l problems but they are l i m i t e d i n the s i z e of problem t h a t can be handled. For i n s t a n c e , the C.G.E. l i n e a r programme i s l i m i t e d to a 18 by 3 0 matrix i n Basic language and a 3 0 by 6 0 matrix i n F o r t r a n . Presumably programmes f o r l a r g e r problems c o u l d be made a v a i l a b l e but the normal t e r m i n a l d e v i c e s , f o r which the above c o s t s were quoted, operate a t slow speeds so t h a t the c o s t s of d a t a i n p u t and s o l u t i o n p r i n t - o u t c o u l d become e x c e s s i v e . T h e r e f o r e , time shared-computers wi t h low speed t e r m i n a l s have l i m i t e d a p p l i c a b i l i t y f o r p r o c e s s i n g OR-type problems. There are two a l t e r n a t i v e s w i t h which to overcome the problem of g e t t i n g l a r g e q u a n t i t i e s of d a t a to the remote computer and the d e t a i l e d a n a l y s i s back to the user. High speed t e r m i n a l s are a v a i l a b l e u s i n g punched paper tape or c a r d readers and h i g h speed p r i n t e r s . For the present t h e i r c o s t s are almost as h i g h as a s m a l l computer, e s p e c i a l l y when i t i s c o n s i d e r e d t h a t they r e q u i r e m u l t i p l e high-grade communication l i n e s . A more s u i t a b l e a l t e r n a t i v e i s f o r the user to maintain the programmes and d a t a base o n - l i n e i n the computer. New d a t a and the e s s e n t i a l r e s u l t s of a run c o u l d be communicated through the slow speed t e r m i n a l at any time. For i n s t a n c e , i n an i n v e n t o r y c o n t r o l system r e c e i p t s and s a l e s c o u l d be entered d a i l y through the t e r m i n a l and each 62 day groups of items c o u l d be processed to o b t a i n stock l e v e l s and r e o r d e r q u a n t i t i e s . A l t e r n a t i v e l y , the programme to o b t a i n r e o r d e r q u a n t i t i e s c o u l d be run p e r i o d i c a l l y and p r i n t e d a t the computer c e n t e r f o r p h y s i c a l d e l i v e r y to the user. The approximate c o s t s of s t o r i n g such a system on l i n e would be $50.00 per month f o r an 8,000 item i n v e n t o r y u s i n g IBM's RAX system r a t e s . Two problems a r i s e w i t h o n - l i n e storage i n a time-shared computer: p r i v a c y and f a i l u r e . To access the user ' s p r o p r i e t a r y programmes and d a t a base, a code i s r e q u i r e d . V i s i t o r s or u n f a i t h f u l employees might o b t a i n the code and make i t a v a i l -able to competitors u s i n g the same t i m e - s h a r i n g s e r v i c e . A l s o , as w i t h any o n - l i n e system there i s the p o s s i b i l i t y of a computer f a i l u r e , and even more c a t a s t r o p h i c , the a c c i d e n t a l e l i m i n a t i o n of the d a t a base. In an i n v e n t o r y system, f o r i n s t a n c e , t h i s would r e q u i r e a p h y s i c a l Inventory count p l u s a search f o r q u a n t i t i e s on order; u n l e s s of course, d u p l i c a t e r e c o r d s were i n c o r p o r a t e d i n the system. In s p i t e of these d i f f i c u l t i e s , the p o s s i b i l i t y of keeping p r o p r i e t a r y OR formulated programmes and the r e q u i s i t e d a t a o n - l i n e at a remote computer e x i s t s and w i l l become i n c r e a s i n g l y a t t r a c t i v e as computers w i t h even l a r g e r memory c a p a c i t i e s and lower p r o c e s s i n g c o s t s become a v a i l a b l e . For the s m a l l company which can process d a t a f o r i t s c o n v e n t i o n a l i n f o r m a t i o n systems more eco n o m i c a l l y on an e l e c t r o n i c computer, the 63 TABLE VI TIME-SHARING COSTS IBM RAX CGE Time-Sharing Terminal R e n t a l B a s i c Terminal Data Set Telephone L i n e Card-read c a p a b i l i t y Paper-tape and card-read $145.00/month 30.00 17.00 166.50 219.50 |130.00/month ( a l l I n c l u s i v e ) Usage Charges Terminal Time CPU Time D i s c Storage $ 12.00/hr. $ 12.00/hr. F i r s t 60 minutes $ 3.00/min. f r e e , t h e r e a f t e r |4.50/min. F i r s t 100,000 $ 2.50/month foyfc©s 1*3?©© f a d d i t i o n a l ' $ . 0 4 5 / f o r 1536 month/disc t r a c k * c h a r a c t e r s * 1 d i s c t r a c k =2880 by t e s . a l t e r n a t i v e means of o b t a i n i n g computer s e r v i c e s i s to l e a s e a s m a l l computer. T h i s p o s s i b i l i t y w i l l be examined i n the f o l l o w i n g s e c t i o n . L e a s i n g Small Computers In keeping w i t h the g e n e r a l r e d u c t i o n i n d a t a p r o -c e s s i n g c o s t s , the c o s t s of l e a s i n g s m a l l computers has f a l l e n markedly. Nearly a l l computer manufacturers have models which l e a s e f o r l e s s than $3,000 per month. One major manufacturer s t a t e d t h a t k0% of i t s business i n 1965 was w i t h companies w i t h l e s s than 500 employees. 1^ Even so, t h i s i s an expensive t o o l f o r most small companies. Before a s s e s s i n g the d e t a i l e d c o s t s of s m a l l computers f o r the s m a l l business engaging i n o p e r a t i o n s r e s e a r c h , the r a t h e r obvious advantages and l i m i t a t i o n s w i l l be examined. The a v a i l a b i l i t y of an o n - s i t e computer as a t o o l f o r o p e r a t i o n s a n a l y s i s i s v e r y a t t r a c t i v e . Mathematical models can be s o l v e d , and s o l u t i o n s t e s t e d , i n a d d i t i o n to the p e r i o d i c running of OR formulated programmes f o r o p e r a t i o n s p l a n n i n g and c o n t r o l . There are no problems of p r i v a c y and s c h e d u l i n g i s accomplished i n t e r n a l l y . However, small computers have l i m i t e d memory c a p a c i t y so t h a t batch W.W. Plnke, C r e d i t and F i n a n c i a l Management, (1966), p. 19. 65 p r o c e s s i n g i s a p r e r e q u i s i t e . A l s o , they have slower computing speeds and t h e r e f o r e they are l e s s e f f i c i e n t e s p e c i a l l y i n p r o c e s s i n g some OR techniques such as l a r g e l i n e a r programmes. In order to j u s t i f y having i t s own computer, the s m a l l b u s i n e s s must have a c o n s i d e r a b l e number of o t h e r t a s k s which i t can more e f f e c t i v e l y process on an e l e c t r o n i c computer than by mechanical means. In having i t s own computer the s m a l l business w i l l no doubt f i n d many a p p l i c a t i o n s f o r i t s c a p a b i l i t i e s . However, i n t h i s l i e s a f r e q u e n t source of t r o u b l e . Not always can the v a s t q u a n t i t i e s of i n f o r m a t i o n obtained be u t i l i z e d by the few managers t h a t most smal l businesses have and the mere c o l l e c t i n g and p r o c e s s i n g of the d a t a r e q u i r e s c o n s i d e r a b l e l a b o u r . In s p i t e of t h i s p o s s i b i l i t y , good systems d e s i g n w i t h e l e c t r o n i c computing c a p a b i l i t y w i l l no doubt improve management's c o n t r o l and p l a n n i n g f u n c t i o n s . However, the c o s t s are r e l a t i v e l y h i g h f o r the small b u s i n e s s . A r e c e n t survey of Canadian computer u s e r s , shows t h a t f o r businesses w i t h up to ten m i l l i o n d o l l a r annual s a l e s , the mean c o s t of e l e c t r o n i c d a t a p r o c e s s i n g as a percentage of revenue, was one percent whereas f o r companies of over f i v e hundred m i l l i o n d o l l a r s i n annual s a l e s , the mean c o s t was about one t e n t h of one p e r c e n t . 1 1 These 13-V.W. Ruskin, Computer User F a c t s , 1967 /68: Part I -Canada, ( 1 9 6 8 ) , E x h i b i t 6 . 66 r e s u l t s Include a l l d i r e c t computer c o s t s such as m a t e r i a l s and s t a f f as w e l l as equipment. In t h i s r e g a r d another r e s u l t of the survey showed t h a t mean s t a f f c o s t s r e p r e s e n t e d f o r t y - n i n e per cent of d i r e c t e l e c t r o n i c d a t a p r o c e s s i n g c o s t s , whereas mean equipment c o s t s were about f o r t y - t h r e e per c e n t . 1 2 With t h i s i n mind and a c c e p t i n g the r e s u l t s of the survey on number of s t a f f f o r lowest c o s t computer equipment, the d i r e c t c o s t s of l e a s i n g and o p e r a t i n g a s m a l l computer would be approximately s e v e n t y - f i v e thousand d o l l a r s per year, assuming common experience i s a guide. T h i s would not i n c l u d e the c o s t of m a i n t a i n i n g s t a f f programmers which we have t r i e d to keep separate i n our assessment of computer s e r v i c e s . Thus, i n s p i t e of the many advantages f o r both o p e r a t i o n s r e s e a r c h and c o n v e n t i o n a l d a t a p r o c e s s i n g , the h i g h c o s t s of l e a s i n g and o p e r a t i n g even sma l l computers l i m i t t h e i r a p p l i c a b i l i t y to s m a l l b u s i n e s s . Computer S e r v i c e s f o r Various Requirements The f o r e g o i n g d i s c u s s i o n has i n d i c a t e d t h a t the e f f e c t i v e n e s s of computer s e r v i c e bureaus, computer time-s h a r i n g and small l e a s e d computers as v e h i c l e s f o r e l e c t r o n i c d a t a p r o c e s s i n g depend on the p a r t i c u l a r company's t o t a l requirements. Besides the few programmes r e q u i r e d f o r I b i d . , E x h i b i t 2 67 implementing o p e r a t i o n s r e s e a r c h , the s m a l l business must have many oth e r a p p l i c a t i o n s f o r a s m a l l computer i f i t i s to c o n s i d e r l e a s i n g . A l s o , care should be taken to Insure t h a t none of the programmes are too l a r g e to be run on a s m a l l computer. Time-sharing i s an a t t r a c t i v e s e r v i c e i f the company has need of q u i c k c a l c u l a t i n g power on a r e g u l a r b a s i s . In t h i s r e g a r d i t i s i n t e r e s t i n g to note the c o n s u l t i n g f i r m s , f o r both e n g i n e e r i n g and management are the most p r e v a l e n t users of the l o c a l t i m e - s h a r i n g s e r v i c e s . Indeed, the c a p a b i l i t y of s o l v i n g or m a n i p u l a t i n g s m a l l mathematical models i s a u s e f u l t o o l f o r the o p e r a t i o n s a n a l y s t but i t i s o n l y a p p l i c a b l e where the s m a l l business i s doing o p e r a t i o n s r e s e a r c h or some other q u a n t i t a t i v e a n a l y s i s such as engineer-i n g on a r e g u l a r b a s i s . The t i m e - s h a r i n g system may a l s o be f e a s i b l e i f the s m a l l company d e s i r e s to keep some of i t s p r o p r i e t a r y programmes and d a t a o n - l i n e f o r random access. In e i t h e r case the t i m e - s h a r i n g s e r v i c e i s l i m i t e d by the d i s t a n c e between the c e n t r a l computer and the p o t e n t i a l user. For p e r i o d i c b a t c h - p r o c e s s i n g of OR formulated p r o -grammes, the computer s e r v i c e bureau i n c l o s e p r o x i m i t y i s almost c e r t a i n l y the most economic source of e l e c t r o n i c d a t a p r o c e s s i n g . CHAPTER V A CASE STUDY: OPERATIONS RESEARCH FOR A SMALL COMPANY As s t a t e d i n the f o r e g o i n g chapters, the q u e s t i o n as to whether o p e r a t i o n s r e s e a r c h can be e f f e c t i v e l y used by sm a l l business can onl y be d e f i n i t e l y answered i n a p a r t i c u l a r case. T h i s chapter d e s c r i b e s a d e t a i l e d study of one company's o p e r a t i o n s , which was made to assess the p r o s p e c t i v e e f f e c t i v e -ness of OR i n a s m a l l company. Company F of the survey was s e l e c t e d f o r t h i s study because of i t s i n t e r e s t i n g o p e r a t i n g problems and the w i l l i n g n e s s of i t s management to cooperate. In p a r t i c u l a r , the Company's business, o r g a n i z a t i o n and o p e r a t i o n s are d e s c r i b e d to, i d e n t i f y o r g a n i z a t i o n a l g o a l s and o p e r a t i n g problems. Subsequently, the e f f e c t i v e n e s s of o p e r a t i o n s r e s e a r c h as an a i d to i n v e n t o r y c o n t r o l i s analysed. Ordering d e c i s i o n r u l e s f o r seven important items are formu-l a t e d and t h e i r use i s simulated u s i n g past p r o d u c t i o n schedules and a c t u a l demand. The simulated r e s u l t s are compared to p a s t r e c o r d s as to i n v e n t o r y l e v e l s , number of orde r s p l a c e d and number of s t o c k o u t s . 1 Some i n d i c a t i o n of p r o s p e c t i v e savings are thus obtained. Recommendations are 1 A stockout occurs when an item, t h a t i s not p r e s e n t l y i n stock, i s r e q u i r e d . 69 made f o r Implementing an i n v e n t o r y c o n t r o l system based on the OR formulated d e c i s i o n r u l e s . In a d d i t i o n , c o n s i d e r a t i o n i s g i v e n to u s i n g o p e r a t i o n s research, to improve s a l e s f o r e -c a s t i n g , p r o d u c t i o n s c h e d u l i n g , and equipment procurement and replacement. In t h i s study, the author was undergoing a l e a r n i n g process and so the study cannot be recommended as a t y p i c a l , good approach to a p p l y i n g OR i n a s m a l l b u s i n e s s . However I t does d i s p l a y some of the p r e v i o u s l y mentioned problems and i t should g i v e the reader a c l o s e r I n s i g h t i n t o the p r a c t i c a l i t y of u s i n g OR i n a s m a l l b u s i n e s s . I. A DESCRIPTION OP THE COMPANY'S BUSINESS Product and Market Environment Company F produces r e l a t i v e l y complex, heavy equip-ment f o r a p a r t i c u l a r phase of one i n d u s t r y . The few dominant companies i n the Canadian i n d u s t r y have, on o c c a s i o n , tended to emphasize c a p i t a l expenditures i n d i f f e r e n t phases of t h e i r o p e r a t i o n s a t d i f f e r e n t times. A l s o the Canadian segment of t h i s i n d u s t r y exports a h i g h p r o p o r t i o n of i t s product and t h e r e f o r e i s s u b j e c t to the v a g a r i e s of world markets and, as in. many other i n d u s t r i e s , when business i s poor they r a r e l y make c a p i t a l expenditures. Consequently, t h i s Company experiences r a t h e r marked 70 f l u c t u a t i o n s i n the demand f o r i t s products and does not experience a s i g n i f i c a n t replacement p a r t s b usiness, which would tend to r e l a t i v e l y reduce f l u c t u a t i o n s i n s a l e s . In a d d i t i o n to the r e s u l t i n g c y c l i c a l and random v a r i a t i o n , demand tends to be sea s o n a l . Recently, the Company has been s u c c e s s f u l i n market-i n g i t s products i n other c o u n t r i e s so t h a t i t i s not as dependent on the Canadian market. There i s a good p o s s i b i l i t y t h a t these s a l e s w i l l tend to dampen the f l u c t u a t i o n s i n t o t a l s a l e s , but i n c r e a s e the problems of f o r e c a s t i n g , which w i l l be d i s c u s s e d l a t e r . C u r r e n t l y the main product l i n e c o n s i s t s of a few models of two l a r g e , complex and r e l a t e d machines, which are produced a t r a t e s o f l e s s than one hundred per year. The Company produces another l i n e of equipment of f a r l e s s importance and i n s l a c k p e r i o d s undertakes custom manufactur-i n g . Design changes are o f t e n i n t r o d u c e d by the r e l a t i v e l y l a r g e e n g i n e e r i n g s t a f f to take e f f e c t of t e c h n o l o g i c a l advances and i n t r o d u c e product improvements. In a d d i t i o n , the Company has undertaken a programme to d e s i g n and b u i l d new types of equipment f o r the p a r t i c u l a r phase of the i n d u s t r y t h a t i t s u p p l i e s , i n order to maintain i t s p o s i t i o n as a l e a d i n g s u p p l i e r of e f f i c i e n t and r e l i a b l e equipment. These development programmes, coupled w i t h marked v a r i a t i o n s 71 i n demand f o r i t s standard products, g i v e r i s e to c o n s i d e r a b l e i n s t a b i l i t y i n the o p e r a t i o n s o f t h i s Company. Company O b j e c t i v e s The main o b j e c t i v e of t h i s Company i s to grow a t a r a p i d pace w h i l e m a i n t a i n i n g an adequate r a t e o f r e t u r n , by i n t r o d u c i n g new types of equipment and by a g g r e s s i v e market-i n g w h i l e c o n f i n i n g i t s e l f to the phase of the i n d u s t r y i t now serv e s . In p a r t i c u l a r the Company i s attempting to achieve a one hundred per cent Increase i n s a l e s w i t h i n the next f o u r years w h i l e m a i n t a i n i n g a f i v e p ercent p r o f i t on s a l e s . A l s o , the Company management f e e l s a s t r o n g r e s -p o n s i b i l i t y towards the w e l f a r e and s a t i s f a c t i o n of i t s employees and t h i s m a nifests i t s e l f i n the o r g a n i z a t i o n and methods of o p e r a t i o n . I I . A DESCRIPTION OP THE COMPANY O r g a n i z a t i o n a l S t r u c t u r e The o r g a n i z a t i o n s t r u c t u r e of t h i s company i s not w e l l d e f i n e d and i s congruous wi t h the r a t h e r i n f o r m a l mode of o p e r a t i o n . O v e r a l l d i r e c t i o n of the Company i s pro v i d e d by the c h i e f e x e c u t i v e o f f i c e r , who a l s o manages the f i n a n c i a l aspects of the Company and p l a y s the l e a d i n g r o l e i n p r o d u c t i o n s c h e d u l i n g . The Company a l s o has an a c t i v e 72 board of d i r e c t o r s which, f o r Instance, makes a l l major c a p i t a l expenditure d e c i s i o n s . The s a l e s manager and the c h i e f engineer a l s o p l a y l e a d i n g r o l e s i n the management of the company. The c h i e f engineer has c o n s i d e r a b l e a u t h o r i t y i n the a r e a of p r o -d u c t i o n p l a n n i n g and c o n t r o l , b e s i d e s s u p e r v i s i n g the e n g i n e e r i n g department. He a l s o i n i t i a t e s most pr o p o s a l s f o r c a p i t a l equipment purchases w i t h s p e c i a l r e c o g n i t i o n f o r the manufacturing requirements of d e s i g n changes. The e n g i n e e r i n g department maintains c l o s e c o n t a c t w i t h customers and the s a l e s d i v i s i o n so as to assess the i n d u s t r y ' s equipment needs and i n i t i a t e d e s i g n improvements. The Company has s u p e r v i s o r s who operate i n the areas of accounting, o f f i c e management, purchasing and p r o d u c t i o n . One superintendent and two foremen s u p e r v i s e the p r o d u c t i o n workers w i t h d i r e c t i o n from the c h i e f e x e c u t i v e o f f i c e r and the c h i e f engineer. There i s a remarkably h i g h worker to s u p e r v i s o r r a t i o - of about t w e n t y - f i v e to one and t h e r e f o r e an unusual amount of r e s p o n s i b i l i t y i s v e s t e d i n the i n d i v i d u a l worker. The assemblers work i n groups of two or three on one type of sub-assembly, whereas the m a c h i n i s t s work I n d i v i d u a l l y a t one machine. The complexity i n v o l v e d r e q u i r e s t h a t the workers have f a i r l y g e n e r a l s k i l l s and a h i g h degree of f a m i l i a r i t y w i t h t h e i r t a s k s . 73 Current Operating P r a c t i c e The p r o d u c t i o n process thus r e t a i n s a f a i r degree of s p e c i a l i z a t i o n . Some p a r t s are machined and f a b r i c a t e d from wrought metal and c a s t i n g s . Other components and p a r t s are purchased ready f o r assembly, but u s u a l l y o n l y i f the Company does not have the c a p a b i l i t y of producing them. G e n e r a l l y the Company p r e f e r s to manufacture a l l components f o r the equipment t h a t they produce. Sub-assemblies are b u i l t a t separate work s t a t i o n s and t r a n s f e r r e d to the f i n a l assembly ar e a where a l s o heavy components, are f a b r i c a t e d . The company has a f a i r l y h i g h investment i n p r o d u c t i o n equipment which up to the present has been mainly standard machines. C u r r e n t l y , the Company i s c o n s i d e r i n g purchasing r a t h e r expensive s p e c i a l i z e d equipment so t h a t i t can p r o -duce some of the components t h a t i t now procures and i n order to i n c r e a s e i t s c a p a b i l i t y f o r the p r o d u c t i o n of d i f f e r -ent types of equipment. The complexity of the main l i n e products r e q u i r e s a l a r g e investment i n raw m a t e r i a l s and purchased components. Each machine r e q u i r e s many thousands of p a r t s and these must be kept on hand to m a i n t a i n the p r o d u c t i o n process. I n v e n t o r i e s f o r standard items are c o n t r o l l e d so as to p r a c t i c a l l y e l i m i n a t e stockouts which would h o l d up pro-d u c t i o n . Many items are stocked by l o c a l s u p p l i e r s , some-times e s p e c i a l l y f o r the Company on a b l a n k e t order b a s i s f o r r e l e a s e as r e q u i r e d , w i t h d e l i v e r y i n one or two days. Other items are manufactured upon r e c e i p t of an order, w i t h v a r y i n g l e a d times of up to about n i n e t y days. Besides i n s u r i n g the a v a i l a b i l i t y of items f o r standard p r o d u c t i o n , the p u r c h a s i n g department must a l s o procure the m a t e r i a l requirements f o r prototype and custom machines. The Company's i n v e n t o r y c o n t r o l cards do not p r o v i d e a p e r p e t u a l r e c o r d of stock l e v e l s because items are not charged out of stock u n t i l the p a r t i c u l a r machine i n which the item was used has been completed and sometimes even 2 later., The cards do, however, provide the t o t a l stock i n i n v e n t o r y p l u s work-in-process. As a s u b s t i t u t e f o r a c t u a l r e c o r d s , the p u r c h a s i n g agent i s made aware of low stock l e v e l s by the warehousemen or, i n the case of raw s t e e l , by the c u t - o f f saw o p e r a t o r . The f i v e men i n v o l v e d make unsystematic checks and base t h e i r a p p r a i s a l on normal p r a c t i c e as v e r y few items have assigned minimum l e v e l s . A l s o , no formal system e x i s t s f o r i n f o r m i n g the purchasing department of the exact item requirements of scheduled and f o r e c a s t p r o d u c t i o n . The schedules are 2 T h i s system was designed mainly f o r purposes of c o s t accounting. The Company uses a job c o s t i n g system In which 75 broken down i n t o sub-assembly requirements and the purchasing agent can determine the m a t e r i a l requirements from the b i l l s of m a t e r i a l f o r each sub-assembly but i n f a c t t h i s i s very r a r e l y done. Consequently, p u r c h a s i n g d e c i s i o n s are based on i n f o r m a l stock l e v e l Information and approximated m a t e r i a l requirements, which sometimes g i v e r i s e to stockouts but more f r e q u e n t l y are manifested i n unreasonably h i g h s t o c k l e v e l s . P r o d u c t i o n Is scheduled f o r orders on hand, once a month f o r the succeeding two months, by the c h i e f e x e c u t i v e o f f i c e r . The schedule f o r the immediately f o l l o w i n g month i s In s u f f i c i e n t d e t a i l to in f o r m each group of assemblers or each m a c h i n i s t as to t h e i r work l o a d f o r the month and i s based on pas t r e c o r d s as to the time taken to perform each a c t i v i t y . Many p a r t s must be produced at l e a s t one month ahead of the machine completion date and so i n g e n e r a l , m a c h i n i s t s ' work i s scheduled one month f o r the succeeding month's f i n a l assembly. However, schedules are o f t e n changed d u r i n g the month due to extenuating circumstances such as customer demands or p r o d u c t i o n problems. T h e r e f o r e , monthly requirements f o r i n v e n t o r y items and machinery a l l l abour c o s t s are accumulated from time cards and a l l m a t e r i a l s are charged out a f t e r completion of the machine, u s i n g b i l l s of m a t e r i a l . Thus i n terms of the c h a r t of accounts, m a t e r i a l i s t r a n s f e r r e d d i r e c t l y from ' i n v e n t o r y ' to ' f i n i s h e d goods' or 'cost-of-goods s o l d * and the i n v e n t o r y r e c o r d cards are e s s e n t i a l l y the i n v e n t o r y accounts f o r each item. 76 c a p a c i t y do not always correspond to o r i g i n a l p l a n s . I I I . OPERATING PROBLEMS The above d e s c r i p t i o n of Company P has p r o v i d e d a back-ground f o r d i s c u s s i n g the r e l a t e d problems of s a l e s f o r e c a s t i n g , p r o d u c t i o n s c h e d u l i n g and i n v e n t o r y c o n t r o l . Some remarks w i l l a l s o be made concerning c a p i t a l equipment expenditures. Besides c o n s i d e r i n g the d i f f i c u l t i e s i n s o l v i n g these problems, the d i s c u s s i o n w i l l demonstrate how improvements i n these areas would s i g n i f i c a n t l y c o n t r i b u t e to the o r g a n i z a t i o n ' s g o a l s of r a p i d growth w i t h adequate p r o f i t s , and a h i g h degree of employee s a t i s f a c t i o n . S a l e s F o r e c a s t i n g To a c o n s i d e r a b l e extent, the problems In p r o d u c t i o n s c h e d u l i n g and i n v e n t o r y c o n t r o l stem from the d i f f i c u l t y o f making ac c u r a t e s a l e s f o r e c a s t s . The d e s c r i p t i o n of the environment i n d i c a t e d some o f the causes of demand i n s t a b i l i t y . The f l u c t u a t i o n s have been extremely d i f f i c u l t to p r e d i c t . The s a l e s d i v i s i o n has a l e a d i n g r o l e i n s a l e s f o r e c a s t i n g but i t s main source of i n f o r m a t i o n i s the c l i e n t s ' o p e r a t i n g e x e c u t i v e s and they are r a r e l y able to advise as to upcoming purchase o r d e r s . There i s a p o s s i b i l i t y t h a t c e r t a i n economic f a c t o r s may g i v e some i n d i c a t i o n of f u t u r e demand 77 and t h i s approach w i l l be d i s c u s s e d l a t e r . I f the volume of s a l e s i s d i f f i c u l t to p r e d i c t , the s a l e s by each type and model would seem v i r t u a l l y i m p o s s i b l e to f o r e c a s t . F o r t u n a t e l y , the bulk of the ord e r s i n any one year are f o r one or two standard models. T e c h n o l o g i c a l trends i n the Company's market g i v e some i n d i c a t i o n as to what these models w i l l be i n each succeeding year. Even so, customers may demand v a r i a t i o n s i n the standard models and these can not be p r e d i c t e d . The a b i l i t y to p r e d i c t s a l e s a c c u r a t e l y would to a l a r g e extent e l i m i n a t e the other problems. Accurate produc-t i o n schedules f o r minimum c o s t o p e r a t i o n s are then more e a s i l y a t t a i n e d . Purchasing plans c o u l d be adhered to wit h l i t t l e chance of stockouts o c c u r r i n g . The s a f e t y stocks t h a t are c a r r i e d f o r unknown demand c o u l d be g r e a t l y reduced and investment i n i n v e n t o r y more c l o s e l y c o n t r o l l e d . Cash requirements would be known and so cash balances c o u l d be reduced. The o b j e c t i v e of employee w e l f a r e i s more r e a d i l y a t t a i n e d as l a y - o f f s are l e s s l i k e l y to occur. These, and other b e n e f i t s suggest t h a t s u b s t a n t i a l e f f o r t s should be a p p l i e d to s a l e s f o r e c a s t i n g . P r o d u c t i o n Scheduling The i n a b i l i t y to f o r e c a s t s a l e s a c c u r a t e l y c r e a t e s s e r i o u s problems i n p r o d u c t i o n s c h e d u l i n g . In the past, 78 products have, on o c c a s i o n , been produced f o r f o r e c a s t e d s a l e s so as to u t i l i z e excess p r o d u c t i v e c a p a c i t y d u r i n g p e r i o d s of slow demand. However, the l a s t time t h i s occured, the company found i t s e l f w i t h a q u a r t e r of a year's pro-d u c t i o n i n f i n i s h e d goods i n v e n t o r y and consequently had to c l o s e the p l a n t f o r some time. T h e r e f o r e , a t present, p r o d u c t i o n i s scheduled to orders i n hand so t h a t the p r o -d u c t i o n r a t e , to a l a r g e extent, f l u c t u a t e s w i t h demand. However, a c c o r d i n g to s t a t e d company p o l i c y , workers are g e n e r a l l y not l a i d - o f f d u r i n g s l a c k p e r i o d s ; nor has the company found i t d e s i r a b l e to have work done by independent machine shops d u r i n g p e r i o d s of peak a c t i v i t y . Instead the Company maintains a r e l a t i v e l y constant labour f o r c e even i f the p r o d u c t i o n r a t e v a r i e s c o n s i d e r a b l y . The p o l i c y of m a i n t a i n i n g f u l l employment d u r i n g times of decreased r a t e s of p r o d u c t i o n does have the advantages of r e d u c i n g employee turnover, m a i n t a i n i n g employee l o y a l t y and thus d e c r e a s i n g the need f o r e x t e n s i v e s u p e r v i s i o n . However, i t has the drawback of c r e a t i n g a h i g h e r l a b o u r content In the c o s t of machines produced i n slow p e r i o d s and i t can e l i m i n a t e the economies achieved by longer run p r o d u c t i o n of p a r t s . Another c o s t of the c u r r e n t p r o d u c t i o n s c h e d u l i n g p o l i c y i s the i n o r d i n a t e amount of e x p e d i t i n g r e q u i r e d of the shop workers and the e n g i n e e r i n g s t a f f i n p a r t i c u l a r . T h i s i s p r i m a r i l y caused by the n e c e s s i t y of changing p r o d u c t i o n schedules i n mid stream, as i t were, to meet ru s h o r d e r s . As a means of overcoming the diseconomies of p r o -d u c t i o n consequent on the i n a b i l i t y to f o r e c a s t s a l e s , the e n g i n e e r i n g department i s I n i t i a t i n g a programme to d e s i g n equipment f o r modular c o n s t r u c t i o n . Thus, each model w i l l be a d i f f e r e n t combination of a l i m i t e d number of sub-assemblies or modules. As a r e s u l t , the s c h e d u l i n g of p a r t and sub-assembly p r o d u c t i o n can be based more e a s i l y on f o r e c a s t demand because investment i n i n v e n t o r i e s and the r i s k o f obsolescence w i l l be r e l a t i v e l y l e s s as compared to producing completed machines f o r i n v e n t o r y . Rush orders can a l s o be completed more q u i c k l y . Even so, the problem of d e t e r m i n i n g the lowest c o s t schedule f o r f l u c t u a t i n g s a l e s would remain. For i n s t a n c e , i f p r o d u c t i o n r a t e i s h e l d r e l a t i v e l y constant, investment i n sub-assembly i n v e n t o r y c o u l d become e x c e s s i v e i n p e r i o d s of s l a c k demand, or back-order d e l a y s c o u l d be damaging i n p e r i o d s of peak demand. A l t e r n a t i v e l y , v a r i a t i o n s i n pro-d u c t i o n r a t e s without employee l a y - o f f s w i l l r e s u l t i n lower average labo u r p r o d u c t i v i t y but f r e q u e n t l a y - o f f s would c r e a t e morale and t r a i n i n g problems. Each one of these a l t e r n a t i v e s r e s u l t s i n a d d i t i o n a l expense, but no doubt some combination of a l l of them i s the l e a s t expensive. The problem i s to determine what t h a t combination i s f o r 80 each p a r t i c u l a r s i t u a t i o n . I d e n t i f y i n g the minimum c o s t p r o d u c t i o n schedules f o r v a r y i n g demand c o u l d o b v i o u s l y l e a d to high e r p r o f i t s . For i n s t a n c e , under c u r r e n t p o l i c y , a f i f t y p e rcent r e d u c t i o n i n p r o d u c t i o n r a t e r e s u l t s i n a one hundred per cent i n c r e a s e i n the labour c o s t of machines produced d u r i n g t h i s p e r i o d , whereas a d i f f e r e n t p o l i c y might r e s u l t i n lower o v e r a l l c o s t s . Another b e n e f i t c o u l d be Increased employee s a t i s -f a c t i o n . Good workers don't l i k e being i d l e and by and l a r g e t h i s Company's p r o d u c t i o n workers are hard working, l o y a l and c o n s c i e n t i o u s . A more r a t i o n a l i z e d p r o d u c t i o n system would 'allow the e n g i n e e r i n g department to concentrate on i t s prime f u n c t i o n of d e s i g n i n g new equipment, the s u c c e s s f u l market-i n g of which, c o n t r i b u t e s to company growth. C a p i t a l Expenditures Determining the f e a s i b i l i t y of investments i n new p r o d u c t i o n machines i s a l a r g e problem because i t i s d i f f i c u l t to p r e d i c t the f u t u r e requirements of p r o d u c t i v e c a p a c i t y . For standard machines such as l a t h e s , the s o l -u t i o n to the problem i s c l o s e l y r e l a t e d to s c h e d u l i n g p o l i c i e s i n t h a t i f p r o d u c t i o n r a t e was h e l d f a i r l y constant, the r e q u i r e d machine shop c a p a c i t y c o u l d be u n i q u e l y determined, whereas i f p r o d u c t i o n r a t e f l u c t u a t e s w i d e l y there i s a t r a d e o f f between overtime p r o d u c t i o n i n p e r i o d s of peak 81 demand and the f i x e d c o s t of i d l e machines d u r i n g slow p e r i o d s . For more s p e c i a l i z e d equipment, matters of g e n e r a l p o l i c y come to the f o r e . Should the Company buy machines to perform complicated and unusual tasks or sub-contract the work? Large o u t l a y s f o r s p e c i a l i z e d machines tend to reduce p r o d u c t i o n f l e x i b i l i t y i n t h a t the Company w i l l attempt to d e s i g n components to t h e i r own p r o d u c t i o n c a p a b i l i t y . That i s , the ownership of c e r t a i n types of equipment o f t e n d e t e r -mines the type of manufacturing t h a t a company w i l l undertake. On the other hand, s u b - c o n t r a c t i n g can be expensive i n terms of time and money. These c o n s i d e r a t i o n s together w i t h c a r e f u l a n a l y s i s of f u t u r e p r o d u c t i o n requirements must be examined i f i n v e s t e d c a p i t a l i s :to y i e l d a h i g h r a t e of r e t u r n and c o n t r i b u t e to r a p i d growth. Replacement of present machinery l s a l s o an important c o n s i d e r a t i o n from an economic and t e c h n i c a l s t a n d p o i n t . Present p o l i c y d i c t a t e s the replacement of many standard machines every three years, but as to whether t h i s i s an optimum p o l i c y has never been a n a l y t i c a l l y determined. Inventory C o n t r o l E f f i c i e n t i n v e n t o r y c o n t r o l Is another v i c t i m of f l u c t u a t i n g s a l e s and changed schedules. Design changes, 82 prototype c o n s t r u c t i o n and Informal and i n a c c u r a t e i n f o r -mation on stock l e v e l s and m a t e r i a l requirements are a l s o f a c t o r s which i n t e r f e r e w i t h o b t a i n i n g the o b j e c t i v e s of minimum c o s t i n v e n t o r y o p e r a t i o n . A m a n i f e s t a t i o n of t h i s s i t u a t i o n i s the r a t h e r h i g h investment i n i n v e n t o r y which ranges between about t h i r t y and f o r t y per cent of y e a r l y m a t e r i a l requirements. Another r e s u l t i s the r a t h e r h i g h c o s t of o p e r a t i n g the c u r r e n t system which i n v o l v e s the s e r v i c e s of e i g h t people. In a d d i t i o n , c o n s i d e r a b l e time i s spent by s t a f f and p r o d u c t i o n personnel i n q u e s t i o n i n g the purchasing agent as to expected d e l i v e r i e s or i n attempting to a s c e r t a i n the stock l e v e l of a c e r t a i n item. In s h o r t , because there i s no w e l l e s t a b l i s h e d system f o r c o n t r o l l i n g i n v e n t o r y , a time-consuming, i n f o r m a l communication network has become e s t a b l i s h e d and r e s u l t s i n c o n s i d e r a b l e l a b o u r i n e f f i c i e n c y , c o n f l i c t and f r u s t r a t i o n . Inventory management has two aspects; d a t a p r o c e s s i n g and d e c i s i o n making. The d e s c r i p t i o n of i n v e n t o r y c o n t r o l i n the pre c e d i n g s e c t i o n c l e a r l y demonstrates t h a t improve-ments i n the i n v e n t o r y c o n t r o l i n f o r m a t i o n system w i l l reduce the c o s t of the Inventory o p e r a t i o n . For t h i s reason, the e n g i n e e r i n g department i s de v e l o p i n g a m a t e r i a l r e q u i r e -ments system. For the present, the d a t a w i l l be manually processed but e v e n t u a l l y i t w i l l be processed once a month 83 on a computer. The system w i l l s t a t e the m a t e r i a l r e q u i r e -ments of scheduled p r o d u c t i o n f o r the f o l l o w i n g two months u s i n g c r o s s i n d e x i n g forms which g i v e the number of times each p a r t i s used i n each sub-assembly. Machine completions w i l l thus have to be scheduled once a month f o r the suc-ceeding three months. T h i s w i l l permit the purchasing department to p l a c e o r d e r s f o r most items to scheduled demand. A c t u a l requirements may be d i f f e r e n t from those scheduled, but c e r t a i n l y the v a r i a n c e w i l l be s m a l l , e s p e c i a l l y when the Company has changed to modular p r o d u c t i o n . However, the items w i t h l o n g e r l e a d times must s t i l l be purchased to f o r e c a s t demand. In e i t h e r case, the problem of determining when and how many of each item to buy would remain. Although the d e c i s i o n s can now be based on b e t t e r i n f o r m a t i o n as to p r o d u c t i o n requirements, the q u a l i t y of these d e c i s i o n s w i l l s t i l l s u f f e r from the l a c k of r e a d i l y a v a i l a b l e , accurate i n f o r -mation on stock l e v e l s . In making these d e c i s i o n s , proper cognizance must be taken of the v a r i a b l e c o s t s i n v o l v e d . The c o s t i n c a r r y i n g a h i g h l e v e l stock must be weighed a g a i n s t the c o s t of p l a c i n g a l a r g e number of o r d e r s and the c o s t of running out of stock. Data on these c o s t s i s not r e a d i l y a v a i l -a ble and c o n s i d e r a b l e e f f o r t i s r e q u i r e d to o b t a i n approx-84 i m a t l o n s . In a d d i t i o n , the d e c i s i o n s must take e f f e c t of s u p p l i e r p o l i c i e s r e g a r d i n g d i s c o u n t s , minimum q u a n t i t i e s , e t c e t e r a , and p l a n t p r o d u c t i o n p r a c t i c e . These f a c t o r s w i l l be c l o s e l y examined i n the study of a few i n v e n t o r y items f o r which an OR approach i s used to formulate o r d e r i n g d e c i s i o n r u l e s . The d e c i s i o n r u l e s are then used i n a s i m u l a t i o n of past experience to determine t h e i r e f f e c t on o r d e r i n g c o s t s and i n v e n t o r y l e v e l s . In t h i s r e g a r d the importance of investment i s raw m a t e r i a l i n v e n t o r y should be noted. For Instance, i f i t were p o s s i b l e to reduce i n v e n t o r y investment by, say, t e n per cent, the r e s u l t i n g r e l e a s e of funds would be s u f f i c i e n t to purchase two major p i e c e s of p r o d u c t i o n machinery. A d d i t i t i o n a l l y improved c o n t r o l over raw m a t e r i a l i n v e n t o r y c o u l d c o n c e i v a b l y reduce the personnel requirements i n the purchasing department and decrease the e f f o r t s of e n g i n e e r i n g and p r o d u c t i o n personnel i n e x p e d i t i n g u r g e n t l y r e q u i r e d items. IV. INVENTORY STUDY T h i s s e c t i o n d e s c r i b e s an attempt to determine the p o t e n t i a l v a l u e of an o p e r a t i o n s r e s e a r c h approach to s o l v i n g a p a r t i c u l a r s m a l l business problem. The problems encountered i n o b t a i n i n g a meaningful estimate of the value 85 are prominent i n the d i s c u s s i o n . Another purpose i s to i l l u s t r a t e the problems of a p p l y i n g OR i n a s m a l l b u s i n e s s . In t h i s s e c t i o n we are concerned w i t h company F's i n v e n t o r y c o n t r o l problems. In a l a t e r s e c t i o n some recommendations w i l l be made f o r u s i n g OR to s o l v e the company's other problems, namely, s a l e s f o r e c a s t i n g , p r o d u c t i o n s c h e d u l i n g and c a p i t a l budgeting. I d e a l l y a random sample of the company's i n v e n t o r y items should be s e l e c t e d f o r d e t a i l e d study. An o p e r a t i o n s r e s e a r c h approach would then be used to formulate optimum o r d e r i n g r u l e s f o r the items i n the sample. These r u l e s would then be t e s t e d by: 1) u s i n g them i n a c t u a l p r a c t i c e f o r perhaps a year, 2) u s i n g them i n a Monte Carlo s i m u l a t i o n , which would r e q u i r e known p r o b a b i l i t y d i s t r i b u t i o n s , 3) simu-l a t i n g t h e i r use on p a s t data. In each case, average stock l e v e l s , number of stockouts and number of orders and s h i p -ments can be determined and compared to past performance to o b t a i n an estimate of the r e d u c t i o n i n v a r i a b l e c o s t s r e s u l t -i n g from the use of the d e c i s i o n r u l e s f o r these items. The t o t a l b e n e f i t s to be d e r i v e d from u s i n g s i m i l a r l y formulated d e c i s i o n r u l e s f o r a l l items can then be estimated from the b e n e f i t s of the random sample and compared to the t o t a l c o s t of f o r m u l a t i n g , implementing and o p e r a t i n g the new c o n t r o l system. In t h i s r egard, c o n s i d e r a t i o n must a l s o be g i v e n to 86 d e s i g n of an i n f o r m a t i o n system f o r g e n e r a t i n g the d a t a to be used i n the d e c i s i o n r u l e s . Some of the c o s t s can be estimated from the experience gained i n the study of the sample items and o t h e r s from the p r e l i m i n a r y d e s i g n of the d a t a p r o c e s s i n g aspect. The d i f f e r e n c e between the b e n e f i t s and the c o s t s would g i v e a good estimate of the v a l u e of the t o t a l system. Of course much of the value would be a t t r i b u t e d to the improved i n f o r m a t i o n system alone. The amount c o u l d be e s t -imated by s i m u l a t i n g the system without the o r d e r i n g r u l e s , and having the p u r c h a s i n g agent make ' o f f - t h e - c u f f d e c i s i o n s f o r o r d e r i n g . These r e s u l t s c o u l d then be compared to the r e s u l t s u s i n g the system w i t h OR formulated d e c i s i o n r u l e s . T h i s might i n d i c a t e t h a t an improved i n f o r m a t i o n system i s a l l t h a t i s necessary to a t t a i n e f f i c i e n t i n v e n t o r y manage-ment. Th e r e f o r e , a l l o c a t i n g the value of the new system between OR formulated o r d e r i n g p o l i c i e s and improved d a t a p r o c e s s i n g i s necessary to determine, i n a s t r i c t sense, the v a l u e of o p e r a t i o n s r e s e a r c h f o r i n v e n t o r y c o n t r o l i n a s m a l l b u s i n e s s . However the two aspects are so c l o s e l y interwoven t h a t d i v i d i n g the b e n e f i t s and c o s t s between them i s both d i f f i c u l t and i n c o n s e q u e n t i a l . Often, the o p e r a t i o n s a n a l y s i s i s necessary to d e s i g n a good i n f o r m a t i o n system; 87 t h a t i s , d e t e r m i n i n g the i n t e r a c t i o n of the o p e r a t i n g v a r i a b l e s s p e c i f i e s the i n f o r m a t i o n t h a t i s r e q u i r e d f o r improved o p e r a t i n g c o n t r o l . Thus, improved i n f o r m a t i o n systems can be a major b e n e f i t of o p e r a t i o n s r e s e a r c h . A l s o i f the d a t a p r o c e s s i n g aspect l s to be run on a computer, the output should, f o r c l e r i c a l e f f i c i e n c y , s p e c i f y order q u a n t i t i e s f o r each item. T h i s i m p l i e s t h a t the computer programme w i l l c o n t a i n o r d e r i n g d e c i s i o n r u l e s . Thus, the d a t a p r o c e s s i n g and o p e r a t i o n s r e s e a r c h aspects are c o n s i d e r e d together. Sample S e l e c t i o n U n f o r t u n a t e l y the ' i d e a l ' approach of random sampling to o b t a i n an estimate of the v a l u e of OR was not found to be p r a c t i c a l f o r purposes of t h i s study. C l o s e r examination of the o r d e r i n g c h a r a c t e r i s t i c s of a wide v a r i e t y of items showed c o n s i d e r a b l e v a r i a t i o n so t h a t f o r sampling purposes the i n v e n t o r y would have to be segregated i n t o sub-populations or the sample s i z e i n c r e a s e d to an unmanageable s i z e f o r our b r i e f study. Rather a few items w i t h r e p r e s e n t a t i v e charac-t e r i s t i c s xvere s e l e c t e d f o r d e t a i l e d study. A l l of these are items used i n e i t h e r or both of the two machines of the main product l i n e (see Table V I I ) . 88 Data A v a i l a b i l i t y and Cost F a c t o r Estimates The ensuing d i s c u s s i o n i s an assessment of the a v a i l -a ble d a t a f o r d e t e r m i n i n g demand c h a r a c t e r i s t i c s , and i n v e n t o r y c o s t s . For t h i s purpose the author spent c o n s i d e r a b l e time d i s c u s s i n g the data, the present o r d e r i n g procedures and s u p p l i e r p o l i c i e s w i t h purchasing department pe r s o n n e l . As p r e v i o u s l y s t a t e d , the company maintains s t o c k c o n t r o l cards f o r each item but the withdrawals are not recorded u n t i l the machine i n which the item was used i s completed, and some-times even l a t e r . T h erefore, the exact time at which an item was removed from raw m a t e r i a l i n v e n t o r y i s not known. For i n s t a n c e , i n one month no items were charged out whereas i n the succeeding month many more items than could p o s s i b l y be used i n one month were charged out. Obviously the w i t h -drawals were spread i n some manner over two months. There i s hoT^ever, a means of approximating h i s t o r i c a l monthly demand. Accurate r e c o r d s are a v a i l a b l e on the number of machines completed i n each month. Also b i l l s o f m a t e r i a l s and i n v e n t o r y r e c o r d s s t a t e whether the machine used one or more of the items under c o n s i d e r a t i o n . By e s t i m a t i n g the approximate time b e f o r e completion t h a t each item i s used, the month i n which i t was removed from stock can be surmised. I t must be emphasized t h a t t h i s H s i very approximate i n t h a t completions can be d e l a y e d f o r some time due to an unusual 8 9 TABLE VII ITEMS FOR DETAILED STUDY P r i c e / u n i t Approximate Leadtime Y e a r l y . . Demand . . Remarks Item A 1 3 2 . 5 0 1 2 0 Item B $ 3 5 0 . 0 0 Item C $ 680.00 Item D | 8 , 2 6 0 . 0 0 Item E $ 1 5 0 . 0 0 Item F $ 5 6 0 . 0 0 Item G $1,740.00 6 0 6 0 5 0 5 0 8 5 6 0 1 day T h i s i s used i n f r a c -t i o n s of a u n i t 1 day G e n e r a l l y requested f i v e at a time by machine shop. 3 weeks Manufactured to order by l o c a l s u p p l i e r . 2 days Stocked l o c a l l y f o r Company on blanke t order. 2 weeks Imported from U.S.A. Long D i s t a n c e 'phone charges = $ 1 . 0 0 . 2 weeks Imported from U.S.A. Long Distance = $ 2 . 5 0 . 3 months Imported from U.S.A. . Long. Distan c e = $2.50. s i t u a t i o n so t h a t an item might have been removed from stock c o n s i d e r a b l y before the estimated time. Also i t does not g i v e the number of items s o l d as replacement p a r t s or the number scrapped. I t does however provide some evidence of the demand c h a r a c t e r i s t i c s of each item f o r f o r m u l a t i n g d e c i s i o n r u l e s and the a c t u a l demands which are used i n the s i m u l a t i o n s . The Company's re c o r d s p r o v i d e d a t a on shipment a r r i v a l s but the q u a n t i t i e s do not always correspond to the amount i n any one ord e r . For i n s t a n c e , two orders may be r e c e i v e d i n one shipment or one order may be d e l i v e r e d i n two shipments. By and l a r g e , the number of shipments r e c e i v e d does correspond to the number of orders p l a c e d . More ac c u r a t e i n f o r m a t i o n on the number and s i z e of orders i s a v a i l a b l e from the o r i g i n a l c o p i e s of orders but the e f f o r t r e q u i r e d i n d i g g i n g them out was judged not to be worth the i n c r e a s e d accuracy o b t a i n a b l e . The c o s t s which are dependent on purchasing p r a c t i c e are not recorded except f o r the p r i c e of each item. A c o n s i d e r a b l e amount of i n v e s t i g a t i o n was r e q u i r e d to produce working estimates. The c o s t to the Company of c a r r y i n g i n v e n t o r y i s p r i n c i p a l l y the o p p o r t u n i t y c o s t of money i n v e s t e d i n i n v e n t o r y . T h i s does to some extent vary w i t h the i n t e r e s t 91 r a t e on bank loans but f o r our g e n e r a l purposes we assume i t to be constant a t twelve per cent, a r a t e used by the Company i n other investment d e c i s i o n s . For items stocked i n the p l a n t , there Is a storage c o s t based on the s i z e of the item and type of storage r e q u i r e d . In our judgement, con-s i d e r i n g the obvious i n a c c u r a c y of other data, the i n c r e a s e d accuracy of s p e c i f i n g t h i s c o s t f o r each item was not worth the e f f o r t . T h e r e f o r e an a d d i t i o n a l 3$ was added to the c a r r y i n g c o s t of a l l items s t o r e d i n the p l a n t . T h i s estimate i s based on an approximate t o t a l v a l u e of these items and the annual c o s t of the space r e q u i r e d . 3 Thus the t o t a l c a r r y i n g c o s t i s 15 per cent per annum of the v a l u e of the item. The c o s t of p l a c i n g orders depends on the item but a g e n e r a l estimate can be used f o r a l l but a few items. T h i s c o s t was c a l c u l a t e d by two methods and takes account o n l y of the employee time i n v o l v e d . In one case the c o s t was c a l -c u l a t e d by d i v i d i n g the t o t a l monthly s a l a r i e s of the employees i n v o l v e d by the number of orders p l a c e d to o b t a i n a c o s t of $2.30 per o r d e r . ^ The other method i d e n t i f i e d the ^Annual c o s t of replacement v a l u e _ 15 - 0 Q _ ^ Average value of i n v e n t o r y i n p l a n t 50TTO" ^ T o t a l S a l a r i e s i n d o l l a r s per month _ $2300 Approximate number of o r d e r s per month 10OO orders = $ 2 . 3 0/order 92 normal o r d e r i n g process and w i t h the h e l p of the employees i n v o l v e d estimated the time r e q u i r e d f o r each step as d e t a i l e d i n Table V I I I . T h i s gave a c o s t of $2.?0 per order f o r normal o r d e r s but there may be e x t r a c o s t s such as f o r long d i s t a n c e telephone c a l l s which can o n l y be I d e n t i f i e d w i t h a p a r t i c u l a r item. The c o s t of being o u t - o f - s t o c k when an item i s requested depends to a l a r g e extent on the time i t takes to get a d d i t i o n a l s t o c k . I f the item i s not a v a i l a b l e from l o c a l stocks and i f there are no s u i t a b l e replacements the c o s t i s extremely h i g h i n t h a t p r o d u c t i o n becomes s t a l l e d . For items w i t h l e a d times of one or two days, the stockout c o s t i s the c o s t of p l a c i n g an a d d i t i o n a l order p l u s the c o s t of d e l a y s and time spent e x p e d i t i n g and r e s c h e d u l i n g work. From our o b s e r v a t i o n s of the shop worker and super-v i s o r y personnel time i n v o l v e d a rough average estimate of twenty d o l l a r s has been made as the o u t - o f - s t o c k c o s t s f o r items t h a t are a v a i l a b l e i n one or two days. Formulation of D e c i s i o n Rules The purpose of the f o l l o w i n g a n a l y s i s i s to formulate d e c i s i o n r u l e s , which do not n e c e s s a r i l y g i v e the optimum r e s u l t s but which p r o v i d e a b a s i s f o r e v a l u a t i n g o p e r a t i o n s r e s e a r c h as a p p l i e d to the i n v e n t o r y problems of Company F. 93 TABLE VI I I ORDERING COST* 1) Warehouseman checks stock l e v e l and r e c o r d s requirements - - - - - - - - $0.40 2) Purchasing Agent phones order and s i g n s purchase order - - - - - - - - $ 0 . 5 0 3) Inventory c l e r k types purchase order - - - - - - - - - - - - - - - - - - $0.20 4) Warehouseman r e c e i v e s and stocks shipment - - - - - - - - - - - $ 1 . 2 5 5) Inventory c l e r k r e c o r d s r e c e i p t and checks i n v o i c e and packing s l i p a g a i n s t order - - - - - - - - - - $0.35 T o t a l Cost $2.?0 *These c o s t s estimated from the time taken to perform the f u n c t i o n and the employee's wage r a t e . 94 Indeed s o p h i s t i c a t e d a n a l y s i s u s i n g standard techniques was not warranted because of the obvious i n a c c u r a c i e s o f the a v a i l a b l e d a t a and the r a t h e r unique o p e r a t i n g c h a r a c t e r i s t i c s of the Company. Ther e f o r e the f o r m u l a t i o n of the d e c i s i o n r u l e s f o r o r d e r i n g each of the seven items i s based on an approach which i s somewhat d i f f e r e n t than t h a t which i s u s u a l l y found i n standard t e x t s on Inventory management. Besides the above g e n e r a l c o n s i d e r a t i o n s , the f o l -lowing premises were made by the author f o r purposes of f o r m u l a t i n g d e c i s i o n r u l e s i n t h i s p a r t i c u l a r i n v e n t o r y study. 1) Orders can be p l a c e d at-semi-monthly reviews. 2) Demand i s known f o r the succeeding one to two months based on p r o d u c t i o n schedules but w i t h c e r t a i n d i s c r e t e p r o b a b i l i t i e s of d i f f e r e n c e s between scheduled demands and a c t u a l usage. 3) The method of keeping i n v e n t o r y stock r e c o r d s w i l l be changed to g i v e an accurate account of q u a n t i t i e s i n raw m a t e r i a l i n v e n t o r y and on order. These premises are based on the f o l l o w i n g c o n s i d e r a t i o n s . In r e g a r d to the f i r s t premise the Company plans to process the i n v e n t o r y c o n t r o l system on a p e r i o d i c b a s i s a t a computer s e r v i c e bureau and t h a t e l i m i n a t e s the p o s s i b i l i t y of a p e r p e t u a l c o n t r o l system. There are a number of f a c t o r s 95 which suggest a semi-monthly review of i n v e n t o r y . A c t u a l usage i s u n l i k e l y to va r y much from schedules i n two weeks. The most economic o r d e r i n g p o l i c y f o r f o u r of the seven items t h a t are d i s c u s s e d below s p e c i f i e s t h a t f o r average demand orde r s should be p l a c e d approximately twice per month. Another c o n s i d e r a t i o n i s the i n v o i c i n g p o l i c y of many s u p p l i e r s . Since statements of account are u s u a l l y o n l y i s s u e d f o r payment at the end of the month, o n l y the items i n i n v e n t o r y a t the end of the month r e p r e s e n t an o p p o r t u n i t y c o s t f o r company funds. Obviously, i n c r e a s i n g the frequency of reviews would add c o n s i d e r a b l y to the c o s t of o p e r a t i n g the c o n t r o l system, e s p e c i a l l y i f i t i s batch processed on a computer. Since the above c o n s i d e r a t i o n s have I n d i c a t e d l i t t l e a d d i t i o n a l b e n e f i t from more fre q u e n t reviews, the author has concluded t h a t the i n v e n t o r y c o n t r o l system should be processed twice per month. The second premise i s the d i r e c t r e s u l t of the Company's plans i n e s t a b l i s h i n g a m a t e r i a l requirements system which can be e a s i l y processed to s t a t e the q u a n t i t i e s of each item t h a t are r e q u i r e d f o r a two month p r o d u c t i o n schedule. However, as s t a t e d e a r l i e r , the a c t u a l usage can be somewhat g r e a t e r through replacement p a r t s a l e s and changed schedules to meet rush o r d e r s . The l a s t premise i s based on the i n f o r m a t i o n r e q u i r e -96 merits of a c l o s e l y c o n t r o l l e d i n v e n t o r y system. Stock l e v e l s and q u a n t i t i e s on order must be e x p l i c i t l y known i n order to determine i f an order should be pl a c e d and how much should be ordered. The f o r m u l a t i o n of the d e c i s i o n r u l e s i s thus based on a system i n ivhich m a t e r i a l requirements are known f o r up to two months i n the f u t u r e , p e r p e t u a l Inventory r e c o r d s are kept o r at l e a s t updated be f o r e each review and the i n v e n t o r y c o n t r o l system i s processed twice a month on an e l e c t r o n i c computer. Item A T h i s item i s f a i r l y r e p r e s e n t a t i v e of much of the Company's purchased m a t e r i a l i n t h a t i t i s a v a i l a b l e from l o c a l stock and i t s demand i s f a i r l y w e l l known from p r o -d u c t i o n schedules. Replacement demand f o r t h i s p a r t l s very s m a l l and the Item has no s u b s t i t u t e i n the company's i n v e n t o r y . In one r e s p e c t i t i s unusual, t h a t i s , I t i s used i n f r a c t i o n s of a u n i t . The t o t a l v a r i a b l e i n v e n t o r y c o s t s are represented i n the f o l l o w i n g e q u a t i o n : T.C. = S c + c P ( x + r ) + p ( r ) c u — > - 1 x u ^ where T.C. = the t o t a l v a r i a b l e monthly i n v e n t o r y c o s t of any d e c i s i o n r u l e s . 97 S. = scheduled demand f o r one month, x = the order q u a n t i t y . C Q = the c o s t of an order independent of the q u a n t i t y . c = the c o s t of c a r r y i n g Inventory f o r one month, as a percentage of item p r i c e P = the p r i c e of the item. p ( r ) = the p r o b a b i l i t y t h a t a c t u a l useage between reviews exceeds the scheduled demand p l u s the r e s e r v e stock. Gu = the o u t - o f - s t o c k c o s t and r = r e s e r v e stock or the stock t h a t i s maintained f o r unexpected demands. The f i r s t term on the r i g h t hand s i d e takes account of the c o s t of o r d e r i n g and i s of course dependent on the number of orders p l a c e d d u r i n g the month. The second term r e p r e s e n t s the c o s t of c a r r y i n g average i n v e n t o r y f o r a month. T h i s assumes t h a t a l l of the r e s e r v e stock remains i n i n v e n t o r y f o r the f u l l p e r i o d and t h i s i s not e n t i r e l y c o r r e c t . There i s a s i g n i f i c a n t p r o b a b i l i t y t h a t some or a l l of the r e s e r v e stock w i l l be used before the end of the p e r i o d but c o n s i d e r i n g t h a t i n g e n e r a l the r e s e r v e s t o c k w i l l be s m a l l compared to scheduled demand, i t can be assumed t h a t i f the r e s e r v e s t o c k i s used i t w i l l be used a t the end of the p e r i o d and t h e r e f o r e the above term r e p r e s e n t s a good 9 8 approximation of the c o r r e c t c o s t . The f i n a l term on the r i g h t hand s i d e i s the expected c o s t of stockouts and as such i s a f u n c t i o n of the amount of r e s e r v e stock. Ignoring, f o r the moment, the stock-out c o s t s , we wish to determine whether or d e r s should be p l a c e d a t each semi-monthly i n v e n t o r y review. Therefore, u s i n g the standard economic order q u a n t i t y formula the f o l l o w i n g order q u a n t i t i e s , x Q , are c a l c u l a t e d f o r average scheduled two month demand of 2 0 u n i t s : x 0 = ^  / 2 ( S.:) c r c P x Q = 5 . 7 i f C Q = $ 2 . 7 0 / o r d e r x Q = 5 - 3 i f G Q = # 2 . 3 0 / o r d e r The d i f f e r e n c e i n the estimated o r d e r i n g costs-* have v e r y l i t t l e e f f e c t on the economic order q u a n t i t y and t h e r e f o r e $ 2 . 5 0 w i l l be used i n a l l subsequent a n a l y s e s . For approx-imate maximum two month demand of 2 6 u n i t s and f o r a slow demand of, say, 1 0 u n i t s the economic order q u a n t i t i e s are 6 . 4 and 3 « 9 u n i t s r e s p e c t i v e l y . Except f o r the l a s t f i g u r e , a l l of these q u a n t i t i e s are approximately one q u a r t e r of the corresponding demand and t h e r e f o r e orders should g e n e r a l l y be p l a c e d at each semi-monthly review. The economic order q u a n t i t y f o r slow demand i s c o n s i d e r a b l y more than one See page 9 1 . 99 q u a r t e r and t h e r e f o r e i t suggests t h a t a minimum order quantity-should be s p e c i f i e d . T h i s w i l l be analysed a f t e r determining how much r e s e r v e stock should be c a r r i e d to p r o t e c t a g a i n s t s t o c k o u t s . There i s no recorded d a t a as to how much a c t u a l demand has v a r i e d from the one month schedules. The o n l y guide i s the d a t a used i n the s i m u l a t i o n of the d e c i s i o n r u l e s (see Table X). These estimates i n d i c a t e t h a t a c t u a l usage exceeded scheduled demand by about one u n i t i n seven of the nine months. However the Company's managers suggested t h a t i n g e n e r a l t h i s frequency would be too hig h and then suggested the f o l l o w i n g p r o b a b i l i t y d i s t r i b u t i o n f o r one month demand of item A: p(D = S) = 0.5 p(D = S + 1) = 0 .4 p(D = S + 2) = o . l where D = a c t u a l t o t a l demand, and S = scheduled demand. S i m i l a r d i s t r i b u t i o n s were obtained f o r many of the other items t h a t are subsequently s t u d i e d . In a l l i n s t a n c e s the d i s t r i b u t i o n i s assumed to be independent of the r a t e of scheduled demand. However, we r e q u i r e the p r o b a b i l i t y d i s t r i b u t i o n f o r h a l f of a month to o b t a i n the p r o b a b i l i t i e s t h a t a c t u a l usage w i l l exceed scheduled demand by v a r i o u s amounts between i n v e n t o r y reviews. I f the semi-monthly d i s t r i b u t i o n i s known, the monthly d i s t r i b u t i o n can be obtained by a bi n o m i a l 6 expansion. In t h i s case the r e v e r s e procedure was accomplished u s i n g a t r i a l and e r r o r method to o b t a i n the approximate semi-monthly d i s t r i b u t i o n which when b i n o m i a l l y expanded g i v e s r i s e to the known monthly p r o b a b i l i t y d i s t r i b u t i o n . The f o l l o w i n g i s the semi-monthly p r o b a b i l i t y d i s t r i b u t i o n t h a t a c t u a l demand, D, w i l l exceed scheduled demand, S, by the i n d i c a t e d amounts. p(D / 2 ^ S / 2 ) = .70 p(D / 2 = S /2+1) = .29 p(D / 2 = S /2+2) = .01 To determine the amount of r e s e r v e stock, r , which should be c a r r i e d , we minimize the c o s t of being out of stock p l u s the c o s t of c a r r y i n g r e s e r v e stock assuming there i s no c a r r y i n g c o s t i f Item A i s used up i n the same p e r i o d i n which i t i s purchased, t h a t i s : T.C. i n Equation 1 i s minimized w i t h r e s p e c t to r . Since the p r o b a b i l i t y d i s t r i b u -t i o n i s not continuous the c a l c u l u s cannot be used. Instead a d e c i s i o n t a b l e , Table IX, i s u t i l i z e d to i d e n t i f y the value of r which r e s u l t s i n the lowest c o s t . Note t h a t the prob-a b i l i t i e s used are taken d i r e c t l y from the semi-monthly p r o b a b i l i t y d i s t r i b u t i o n . M.K. S t a r r and D.W. M i l l e r , Inventory C o n t r o l : Theory and P r a c t i c e , ( 1 9 6 2 ) , pp. 116-119. 101 The t a b l e i n d i c a t e s t h a t the p o l i c y of buying one u n i t more than scheduled demand g i v e s the l e a s t t o t a l c o s t . I f scheduled demand i s , say, 2.5 u n i t s the above c o s t matrix suggests t h a t , because of the low c o s t of c a r r y i n g one u n i t f o r two weeks, an order should be p l a c e d f o r f o u r u n i t s assuming no stock i s i n i n v e n t o r y . TABLE IX RESERVE STOCK DECISION TABLE Reserve Stock A c t u a l Demand, D V a r i a b l e Cost of P o l i c y P o l i c y S + r S S + 1 S + 2 |/review p e r i o d S 0.0 20.0 20.0 6.00 S + 1 0 . 8 3 0.0 20.0 0 . 7 8 S + 2 1 . 6 6 0 . 8 3 0.0 1.40 P r o b a b i l i t y .70 .29 .01 But what i s the minimum order q u a n t i t y ? The a n a l y s i s i n d e t e r m i n i n g the most economic order q u a n t i t i e s f o r v a r i o u s demand l e v e l s i n d i c a t e d t h a t d u r i n g p e r i o d s of slow demand orders f o r item A should be p l a c e d o n l y once a month. Thus we determine the scheduled demand r a t e a t which the c o s t of c a r r y i n g i n v e n t o r y f o r an e x t r a h a l f month i s l e s s than the expected s a v i n g of not having to p l a c e another order a t the next review, t h a t i s , (S + 1) cP = p(D>S + l ) C r _ _ _ _ _ _ _ _ - 4 •S =" 4 In other words, i f the scheduled requirements f o r the succeeding month i s f o u r u n i t s or l e s s , o n l y one order should he p l a c e d . The d e c i s i o n r u l e s can now be s t a t e d based on the above a n a l y s i s : Reorder i f I < S + 1' Order quantity, x 0 = S + 1 - I, i f S > 2 x Q = 2(S + 1) - I, i f S =" 2 f where I = q u a n t i t y i n i n v e n t o r y . As s t a t e d a t the beginning the item must be ordered i n whole u n i t s although i t i s used and may be scheduled i n f r a c t i o n s of u n i t s . More d e t a i l e d a n a l y s i s would be r e q u i r e d to s t a t e the d e c i s i o n r u l e s i n f r a c t i o n s . C o n s i d e r i n g the low c o s t of c a r r y i n g t h i s item, i t i s s u f f i c i e n t to s t a t e t h a t the order q u a n t i t y should be f o r the next l a r g e s t whole u n i t , although a d m i t t e d l y t h i s may not be the optimum p o l i c y . The o r d e r i n g d e c i s i o n r u l e s may not r e s u l t i n the ab s o l u t e minimum c o s t i n v e n t o r y o p e r a t i o n f o r other reasons. For example, the p r o b a b i l i t y d i s t r i b u t i o n of a c t u a l usage 103 exceeding scheduled demand by v a r i o u s amounts i s not w e l l known and almost a s s u r e d l y v a r i e s w i t h the a c t i v i t y l e v e l . A l s o the c o s t of stockouts i s a very rough estimate which v a r i e s w i t h the s i t u a t i o n , although s e n s i t i v i t y a n a l y s i s on the d e c i s i o n t a b l e (Table IX) i n d i c a t e s t h a t even a 100% e r r o r would not change the r e s u l t . To assess the value of t h i s d e c i s i o n r u l e as compared to past p r a c t i c e , the l a s t t e n months experience was simulated i n Table X u s i n g a c t u a l p r o d u c t i o n schedules of completed machines and estimates of item withdrawals. Note, t h a t as i s i n the past, the p r o d u c t i o n schedules are f o r one month, o n l y . Using the OR formulated d e c i s i o n r u l e s would have reduced the value of the average semi-monthly i n v e n t o r y l e v e l by $700 and thus r e s u l t e d i n a t o t a l s a v i n g of $33«00 i n the seven months o p e r a t i o n a f t e r the d e c i s i o n r u l e s took e f f e c t . T h i s does not i n c l u d e the p o s s i b i l i t y t h a t stockouts occurred i n a c t u a l p r a c t i c e because the d a t a i s too i n a c c u r a t e to even suggest t h i s . The f o r e g o i n g d e s c r i p t i o n has been i n c o n s i d e r a b l e d e t a i l . The a n a l y s i s of the f o l l o w i n g items w i l l be d e s c r i b e d o n l y to the extent of o u t l i n i n g v a r i a t i o n s due to d i f f e r e n t c h a r a c t e r i s t i c s . For i n s t a n c e , the s i m u l a t i o n t a b l e s are the same f o r a l l items and t h e r e f o r e the s i m u l a t i o n s f o r the remaining items w i l l not be d i s p l a y e d . 104 TABLE X INVENTORY SIMULATION - ITEM A Month Scheduled D e c i s i o n Amount End of A c t u a l Estimated Demand Rule Used p e r i o d Orders A c t u a l . Orders . . . . . Inventory . .Inventory June J u l y 1 5 . 2 5 0 J u l y 2 5 . 2 5 0 Aug. 1 4 . 5 0 Aug. 2 k.5 0 Sept. 1 4 . 2 0 Sept. 2 4 . 2 4 . 0 Oct. 1 5 . 2 6 . 0 Oct. 2 5 . 2 6.0*(8.0) Nov. 1 6 . 9 0 Nov. 2 6 . 9 5 . 0 Dec. 1 5 . 8 5 . 0 Dec. 2 5 . 8 5 . 0 Jan. 1 6 . 9 8 . 0 Jan. 2 6 . 9 8 . 0 Feb. 1 5 . 5 6 . 0 Feb. 2 5 . 5 5 . 0 Mar. 1 7 . 7 9 . 0 Mar. 2 7 . 7 8 . 0 2 0 . 0 2 0 . 0 2 . 1 1 7 . 9 0 1 7 . 9 2 . 1 1 5 . 8 0 1 5 . 8 4 . 8 1 1 . 0 0 1 1 . 0 4 . 8 6 . 2 0 6 . 2 4 . 6 1 . 6 0 1 . 6 4 . 6 1 . 0 4 . 0 1 . 0 6 . 7 0 . 3 1 0 . 0 k.3 6 . 7 7 . 6 1 0 . 0 7.6 4 . 9 2 . 7 0 2 . 7 4 . 9 2 . 8 1 2 . 0 9 . 8 6 . 3 1 . 5 0 3 . 5 6 . 3 0.2 20.0 17.2 7 . 4 0 . 8 7 . 0 1 6 . 8 7 . 4 1 . 4 0 9 . 4 5 . 9 1 . 5 0 3 . 5 5 . 9 0 . 6 1 5 . 0 1 2 . 6 8 . 1 1 . 5 0 4 . 5 8 . 1 1 . 4 5 . 0 1 . 4 105 Item B T h i s item i s used i n n e a r l y a l l machines of the main product l i n e , but there i s v e r y l i t t l e replacement demand f o r the machined p a r t which i s made from t h i s item. Average demand f o r the past eighteen months has been about f i v e per month. I t i s stocked by a l o c a l s u p p l i e r w i t h d e l i v e r y i n one or two days. Item B i s machined by the Company i n l o t s of s i x a t a time. There, i s some q u e s t i o n as to whether s i x i s the most economic q u a n t i t y to machine a t one time f o r a l l p r o d u c t i o n r a t e s . T h i s problem w i l l not be analyzed here as i t i s a p r o d u c t i o n problem and thus e n t a i l s an i n v e s t i g a t i o n of i t s i n t e r a c t i o n w i t h the s c h e d u l i n g of other machining. S u f f i c i e n t to say t h a t s i x of these items can be machined i n one set up and t h e r e f o r e the present s c h e d u l i n g p o l i c y w i l l be assumed to be c o r r e c t . Obviously, there i s no b e n e f i t i n buying i n q u a n t i t i e s of l e s s than s i x . However, the p o s s i b i l i t y of o r d e r i n g more than s i x at a time must be examined. For maximum p r o d u c t i o n demand of twelve i n two months, the most economic order q u a n t i t y , x i s : x° n/^ FP = z-6 - - 5 T h e r e f o r e , s i x u n i t s should be ordered at one time. Since the machine shop foreman knox-js f o r some time 1 0 6 ahead when these p a r t s w i l l be machined and the l e a d time is a few days, t h i s item should not be stocked as rax\r m a t e r i a l on a r e g u l a r b a s i s but ordered on advice from the foreman to meet the p r o d u c t i o n schedule of the machine shop. Ther e f o r e the d e c i s i o n r u l e may be s t a t e d as: Reorder, as r e q u i r e d by the machine shop on three days n o t i c e from the foreman. Order q u a n t i t y , x Q = 6 . The s i x u n i t s would then be machined soon a f t e r they a r r i v e d in the p l a n t and t h e r e f o r e they would not be c a r r i e d i n raw m a t e r i a l i n v e n t o r y . The experience of the past twelve months i n d i c a t e s t h a t the average end of the month i n v e n t o r y of item B was ten u n i t s and t h a t ten o r d e r s were p l a c e d . In a d d i t i o n the r e c o r d s suggest t h a t a stockout o c c u r r e d at l e a s t once. The imputed c o s t s of l a s t year's performance are $25.00 f o r o r d e r i n g , $ 5 2 0 . 0 0 f o r c a r r y i n g charges f o r a t o t a l c o s t of $ 5 ^ 5 . 0 0 versus an expected c o s t of $ 2 5 . 0 0 f o r o r d e r i n g i f the d e c i s i o n r u l e had been f o l l o w e d . Thus a saving of $520.00 per year c o u l d be expected by u s i n g t h i s d e c i s i o n r u l e . Item G T h i s Item i s a l s o used i n a l l machines i n the main product l i n e . Item C i s made to order by the s u p p l i e r w i t h d e l i v e r y i n about three weeks from r e c e i p t o f . o r d e r . Company p r a c t i c e i s to machine these one a t a time. Scheduled demand i s known f o r two months at end-of-the-month i n v e n t o r y reviews and f o r s i x weeks a t ' m i d d l e - o f -the-month reviews whereas the l a p s e d time between p l a c i n g one order and r e c e i v i n g the next i s f i v e weeks. Therefore, purchases can be made to scheduled demand, S, but w i t h the f o l l o w i n g p r o b a b i l i t i e s t h a t a c t u a l usage w i l l exceed scheduled demand f o r the month. p(D = S) = 50% p(D = S+l) = k0% p(D = S+2) = 10% These p r o b a b i l i t i e s are based on past d a t a and. management's s u b j e c t i v e o p i n i o n as e x p l a i n e d f o r Item A. To be s t r i c t l y c o r r e c t , the d i s t r i b u t i o n should be a d j u s t e d to the f i v e week l e a d time p l u s review p e r i o d but s i n c e the d i f f e r e n c e between one month and f i v e weeks i s s m a l l and s i n c e the accuracy i s poor, the above d i s t r i b u t i o n g i v e s the approximate p r o b a b i l i t i e s t h a t a c t u a l demand, D, w i l l exceed scheduled demand, S, i n the f i v e week p e r i o d between p l a c i n g one order and r e c e i v i n g the next. The v a r i a b l e i n v e n t o r y c o s t f o r t h i s item i s , T . C . = S c + c P (X + r ) + p ( T ) K - - 6 X 2 ° where the symbols have the same meanings as used i n Equation 1 w i t h the e x c e p t i o n t h a t K Q i s the o u t - o f - s t o c k c o s t as i t i s much l a r g e r because t h i s item i s not a v a i l a b l e from stock. 108 The a c t u a l c o s t Is p r a c t i c a l l y i m p o s s i b l e to determine by d i r e c t measurement. I t may be imputed from management's p o l i c y as to the r e s e r v e s t o c k normally c a r r i e d I f i t c o u l d be assumed t h a t management e x p l i c i t l y knows the c o s t of c a r r y i n g the re s e r v e stock. In t h i s case i t was not p o s s i b l e to impute a c o s t because of the inadequacy of the da t a . T h e r e f o r e an a r b i t r a r i l y h i g h f i g u r e of $2000.00 i s used as the c o s t of running out of item C. The accuracy of t h i s f i g u r e c o u l d be improved as b e t t e r d a t a i s generated through o p e r a t i o n of the proposed i n v e n t o r y c o n t r o l system. Using E q u a t i o n 6, the economic order q u a n t i t y , x, i s 1.7 u n i t s f o r the average monthly demand of 5 u n i t s . Since t h i s i s l e s s than one h a l f of the average monthly demand, item C should be ordered a t each review p e r i o d w i t h no minimum q u a n t i t y . The amount of r e s e r v e stock, r , to be c a r r i e d can be determined u s i n g a d e c i s i o n t a b l e s i m i l a r to Table IX. I t s p e c i f i e s a r e s e r v e stock of two as the most economic. Therefore -the d e c i s i o n r u l e s f o r o r d e r i n g item C a r e : Reorder i f I + 0 S + 2; Order q u a n t i t y , x Q = ( S + 2 ) - ( I + 0 ) , where 0 =•the amount on order. Simulated use of these r u l e s u s i n g d a t a on the Company's o p e r a t i o n s f o r the past seven months r e s u l t e d i n an average e n d - o f - p e r i o d i n v e n t o r y of one, whereas the 109 estimated a c t u a l i n v e n t o r y l e v e l was about e i g h t u n i t s on the average. The p r o s p e c t i v e c o s t saving i s then approximately $400.00 f o r the seven months. Item D T h i s item i s used i n most but not a l l of the machines produced by the company at an average r a t e of f o u r per month. I t i s stocked f o r the Company l o c a l l y so t h a t d e l i v e r y i s made w i t h i n two days. A group of f i t t e r s prepare these items, g e n e r a l l y one a t a time, f o r i n s t a l l a t i o n i n the f i n i s h e d product. The h i g h p r i c e and two day d e l i v e r y time of t h i s item I n d i c a t e s t h a t i t should be ordered one a t a time as r e q u i r e d by the f i t t e r s . However, because of a s p e c i a l p urchasing arrangement, the Company i s not i n v o i c e d f o r item D u n t i l i t i s taken i n t o the p l a n t to be worked on. Th e r e f o r e o r d e r s should be p l a c e d a t each review p e r i o d to meet scheduled demand. The stockout c o s t of t h i s item i s somewhat high e r because the men t h a t work on i t have v e r y l i t t l e e l s e to do i f one i s not a v a i l a b l e f o r f i t t i n g . A c o s t of f i f t y d o l l a r s i s t h e r e f o r e assigned to sto c k o u t s . The p r o b a b i l i t y of a c t u a l demand exceeding scheduled demand i s somewhat l e s s than f o r the three p r e v i o u s items, having occured o n l y three times i n the past twelve months. Therefore, u s i n g f i f t e e n per 110 cent as the p r o b a b i l i t y of running out of stock d u r i n g the review p e r i o d , a n a l y s i s by means of a d e c i s i o n t a b l e i n d i c a t e s t h a t i n v e n t o r y a t the s t a r t of the review p e r i o d should be * equal to scheduled demand p l u s one u n i t f o r r e s e r v e stock. Thus the d e c i s i o n r u l e i s : Order i f I < S. + 1 Reorder q u a n t i t y , x = S, + 1 - I. Simulated use of these r u l e s f o r the p a s t eleven months experience i n d i c a t e s a saving of about $300.00. T h i s r e s u l t l s v e r y i n t e r e s t i n g because the p o t e n t i a l saving i s r a t h e r s m a l l f o r such a h i g h p r i c e d item. The main reason f o r t h i s i s the s u p p l i e r ' s p o l i c y on i n v o i c i n g which r e s u l t s i n a r a t h e r low c a r r y i n g c o s t . There i s the p o s s i b i l i t y t h a t a hidden charge e x i s t s f o r t h i s p r i v i l e g e but the author was not able to determine i t e x p l i c i t l y . Item E T h i s item i s a matching set of p a r t s manufactured by an American s u p p l i e r to the Company's o r d e r s . Average demand i s about f o u r s e t s per month. To take advantage of the maximum q u a n t i t y d i s c o u n t an order i s p l a c e d f o r s i x t y -f o u r s e t s but s m a l l e r q u a n t i t i e s can be released" as r e q u i r e d w i t h d e l i v e r y i n two weeks. Therefore, the problem i s to determine the optimum frequency of r e l e a s e s and the I l l most economic r e s e r v e stock. The economic order q u a n t i t y i s 4 . 1 s e t s f o r average demand of f o u r per month, w i t h the order c o s t of $ 4 . 5 0 s u g g e s t i n g t h a t orders should be p l a c e d once a month so th a t the e f f e c t i v e l e a d time w i l l be s i x weeks. The p r o b a b i l i t i e s t h a t a c t u a l usage, D, w i l l exceed scheduled monthly demand, S, i n s i x weeks a r e : p(D =" 1.5S) = . 50 p(D = 1.5S+1) = .35 p(D = 1.5S+2) = . 1 0 p(D = 1 .5S+3) = .05 Using an a r b i t r a r i l y h i g h stockout c o s t of $2000, the d e c i s i o n t a b l e i n d i c a t e s t h a t three e x t r a s e t s should be c a r r i e d i n stock. However there i s the p o s s i b i l i t y of o r d e r i n g again at the mid-month review i f the usage i n the f i r s t h a l f of the month exceeds scheduled demand. Using the c o n v o l u t i o n s of the above p r o b a b i l i t y d i s t r i b u t i o n , the l i k e l i h o o d t h a t a c t u a l usage w i l l exceed scheduled demand i n the remaining one month by more than two i s n e g l i g i b l e i f a c t u a l usage D e l i v e r i e s are u s u a l l y requested by long d i s t a n c e telephone c a l l . ($1.00) and there i s a l s o a f i x e d customs brokerage charge ( $ 1 . 0 0 ) equals or i s l e s s than scheduled demand i n the f i r s t two weeks of the month. Thus, r a t h e r than c a r r y three e x t r a s e t s , two e x t r a s e t s are c a r r i e d and a mid-month-order i s pl a c e d i f usage exceeds scheduled demand i n the i n i t i a l two weeks a f t e r p l a c i n g an order. Reducing the p r o b a b i l i t i e s to two week p e r i o d s shows t h a t p (D>S /2) = 0 . 2 0 . The expected c o s t of the a d d i t i o n a l order i s $ 0 . 9 0 whereas the expected c o s t of c a r r y i n g the e x t r a u n i t i s $ 1 . 5 0 . T h e r e f o r e the f o l l o w i n g d e c i s i o n r u l e a p p l i e s : Order i f I < B + 2 Order q u a n t i t y , x Q = 1.5S + 2 - I. Simulated use of these d e c i s i o n r u l e s on the past nine months' p r o d u c t i o n schedules and i n v e n t o r y withdrawals r e s u l t e d i n a r e d u c t i o n of average i n v e n t o r y from f i f t e e n to three s e t s . The r e s u l t a n t expected savings i n i n v e n t o r y c o s t s f o r the ni n e months are $ 1 7 0 . 0 0 . Item F The average demand f o r t h i s item i s seven u n i t s per month. The demand tends to f l u c t u a t e widely and ranges between three and ten per month because i t i s sometimes r e p l a c e d by d i f f e r e n t brands and the number used i n each machine can var y . The c u r r e n t o r d e r i n g p r a c t i c e i s to p l a c e b l a n k e t orders from which r e l e a s e s are p e r i o d i c a l l y i s s u e d . 113 The delivery i s effected i n about two weeks after issuing a release. The order cost f o r th i s item i s $6.00 because of long distance telephone and brokerage charges. The economic order quantity f o r average demand i s 3.5 units. This r e s u l t i n d i -cates that orders should be placed twice every month. There i s a s i g n i f i c a n t p r o b a b i l i t y that scheduled demand can be exceeded by up to three units i n one month. Therefore without further discussion of the analysis which i s similar to item E the decision rules are stated: Order i f , I<S + 3 Order quantity, x = S + 3 - I, I f x =3 , o o X Q = 3» otherwise The minimum order quantity i s included because the supplier i s opposed to sending just one or two units. Simulated use of these rules r e s u l t s i n an average inventory of four units compared to actual average stock of 13 units i n the past s i x months. The cost of ordering plus carrying charges would have been $234.00 using the decision rules, as compared to the actual estimated cost of $569.00. Item G Item G i s a rather complicated component which i s made to the Company's orders. This l a s t item to be dealt 114 w i t h i s the most d i f f i c u l t from a q u a n t i t a t i v e p o i n t of view. I t i s an expensive item, $ 1 , 7 6 0 per u n i t , w i t h a l o n g l e a d time of n i n e t y days from r e c e i p t of order. Twenty-five u n i t s are ordtered a t one time so as to take advantage of the maximum q u a n t i t y d i s c o u n t , and d e l i v e r i e s are scheduled as r e q u i r e d . I f the i n v e n t o r y l e v e l s t a r t s to b u i l d up the d e l i v e r i e s can be delayed i f s u f f i c i e n t n o t i c e i s g i v e n . For our purposes we have assumed t h a t items can be r e l e a s e d as r e q u i r e d f o r d e l i v e r y i n three months, so t h a t the e f f e c t i v e l e a d time i s three and one h a l f months i f r e l e a s e s are made at every Inventory review. P r o d u c t i o n schedules w i l l extend f o r o n l y two months ahead so t h a t o r d e r s f o r t h i s item can not be based on scheduled demand. S t a t i s t i c a l f o r e c a s t i n g techniques, such as e x p o n e n t i a l smoothing, have been t r i e d but w i t h v e r y poor r e s u l t s . T h e r e f o r e orders must be based on managements* s u b j e c t i v e estimate of four-month demand w i t h proper cog-n i z a n c e of two-month scheduled requirements. F o r t u n a t e l y t h i s item i s used i n almost a l l machines so t h a t demand i s r e l a t i v e l y s t a b l e . The q u e s t i o n remains of how f r e q u e n t l y the d e l i v e r i e s should be scheduled. The economic order q u a n t i t y i s 2.8 g u n i t s f o r average demand u s i n g an order c o s t of $ 1 6 . 0 0 . The o r d e r i n g c o s t i n c l u d e s brokerage charges, $ 1 . 0 0 , l o n g d i s t a n c e telephone charges, $ 2 . 5 0 and the c o s t of executive time i n p r e d i c t i n g demand, $ 1 2 . 0 0 . 115 Therefore orders should be p l a c e d at every review p e r i o d to meet the maximum expected, three and one h a l f month r e q u i r e -ments. The minimum r e l e a s e order t h a t can be p l a c e d as s e t by the s u p p l i e r i s 3 u n i t s . The r e s u l t i n g d e c i s i o n r u l e s may be s t a t e d as f o l l o w s : Order i f P(S) ^ I + 0 Order q u a n t i t y x = P ( S ) - (I + 0), i f x Q ^ 3 x Q = 3 , otherwise where P(S) = maximum expected demand f o r 3t months, r e c o g n i z i n g p r o d u c t i o n schedules f o r up to 2 months, and 0 = q u a n t i t y on order. The simulated use of these r u l e s i s not v e r y mean-i n g f u l because there are of course no r e c o r d s as to the maximum expected demand. However by u s i n g scheduled demand f o r 60 days and maximum p o s s i b l e demand f o r the remaining 45 days of the l e a d time, a s i m u l a t i o n was made and compared to a c t u a l performance. Average i n v e n t o r y would have been reduced by f i v e u n i t s i f the o r d e r i n g had been based on the d e c i s i o n r u l e s . The r e s u l t a n t c o s t s a v i n g i s estimated a t $1400 f o r twelve months. E v a l u a t i o n of the Proposed Inventory C o n t r o l System The f o r e g o i n g a n a l y s i s was based on the premise t h a t i n f o r m a t i o n on scheduled requirements, Items on order and stock l e v e l s would be r e a d i l y a v a i l a b l e f o r use i n the d e c i s i o n r u l e s . Thus the c o s t and b e n e f i t s of improved da t a c o l l e c t i o n and g e n e r a t i o n must be assessed i n order to determine the p r a c t i c a l i t y of the new i n v e n t o r y c o n t r o l system. For t h i s reason, some recommendations f o r imple-menting the c o n t r o l system are made p a r t i c u l a r l y w i t h r e s p e c t to g e n e r a t i n g and p r o c e s s i n g the r e q u i r e d d a t a . Subsequently the c o s t s of implementing and o p e r a t i n g the system are approximated and compared to the b e n e f i t s to be d e r i v e d from o p e r a t i n g the system f o r a three year p e r i o d . The requirements of the d a t a p r o c e s s i n g phase a r e : 1) m a t e r i a l requirements of scheduled p r o d u c t i o n f o r the succeeding two months must be e x p l i c i t l y s t a t e d f o r a l l important items,^ 2) the stock l e v e l and amount on order f o r every important item must be known at each review p e r i o d , and 3) the system must be e a s i l y updated to take e f f e c t of d e s i g n and p r i c e changes. As mentioned e a r l i e r , the e n g i n e e r i n g department i s undertaking a programme to develop an e a s i l y processed system f o r determining the m a t e r i a l requirements of p r o d u c t i o n schedules. T h i s r e p r e s e n t s a f o r m i d a b l e task because of the l a r g e number of items and the frequency of d e s i g n changes which must be e a s i l y i n c o r p o r a t e d . One method of approaching t h i s problem i s to use a matrix f o r m u l a t i o n s i m i l a r to the Lieberman p r o p o s a l f o r d e s i g n i n g i n f o r m a t i o n s y s t e m s . 1 0 Using t h i s 9Important items are those f o r which there i s a l a r g e enough d o l l a r volume to make i t s f o r m a l c o n t r o l worthwhile. For i n s t a n c e , i n c l u s i o n of odd s i z e s of nuts and b o l t s i s 117 method, a l l m a t e r i a l i s c o n s i d e r e d i n f o u r l e v e l s , namely, raw m a t e r i a l , p a r t s , sub-assemblies and f i n i s h e d machines. Matrix m u l t i p l i c a t i o n w i l l , f o r example, g i v e the amount of each item of raw m a t e r i a l used i n a g i v e n s e t of sub-assemblies, or the numbers of each p a r t r e q u i r e d f o r a c e r t a i n p r o d u c t i o n schedule. A l s o d e s i g n changes can be e a s i l y i n c o r p o r a t e d and the m a t r i x f o r m u l a t i o n i s v e r y amenable to computer p r o c e s s i n g i n t h a t each p a r t or sub-assembly used i n the machine Is i d e n t i f i e d by i t s p o s i t i o n i n a matrix. The development and use of t h i s p r o p o s a l i s i l l u s t r a t e d i n Appendix I I . Using t h i s method the f i r s t and t h i r d requirements of the d a t a p r o c e s s i n g phase would be accomplished. A method of g e n e r a t i n g stock l e v e l i n f o r m a t i o n i n c l u d i n g q u a n t i t i e s on order i s an important c o n s i d e r a t i o n . The Company's present method of keeping i n v e n t o r y r e c o r d s would have to be changed so as to provide accurate, r e a d i l y a v a i l -a b l e d a t a on r e c e i p t s and withdrawals. T h i s would i n v o l v e the a d d i t i o n of a check-out system f o r m a t e r i a l being t r a n s -f e r r e d from i n v e n t o r y to p r o d u c t i o n . A l t e r n a t i v e l y , a semi-monthly i n v e n t o r y count i s p o s s i b l e but probably more expensive. A l s o , the q u a n t i t i e s a l r e a d y on order but not y e t r e c e i v e d must be known and l i k e l y c o u l d be obtained from not regarded as worthwhile. 1 0 I . J . Lieberman, "A Mathematical Model f o r Integrated. Business Systems," (1956). 118 w i t h i n the d a t a p r o c e s s i n g system u s i n g past order d e c i s i o n s and r e c e i p t r e c o r d s . Ordering r u l e s , f o r the approximately two thousand items of importance, must be formulated. The seven items s t u d i e d provide a c l e a r i n d i c a t i o n of the v a r i e t y i n v o l v e d but a l s o they are f a i r l y r e p r e s e n t a t i v e so t h a t the r u l e s f o r most other items can be based on the a n a l y s i s a l r e a d y done. Thus the o r d e r i n g d e c i s i o n r u l e s f o r many of the other items, perhaps even a m a j o r i t y , can be based on the order r u l e of one or more of the seven items w i t h some adjustment f o r p r i c e s . Even so, each one of the items would have to be examined to a s c e r t a i n t h e i r r e l e v a n t c h a r a c t e r i s t i c s . D e t a i l e d a n a l y s i s w i l l be necessary to develop o r d e r i n g r u l e s f o r the o t h e r items. Also the o r d e r i n g p o l i c i e s w i l l have to be reviewed p e r i o d i c a l l y to take e f f e c t of changed s u p p l i e r p o l i c i e s , d i f f e r e n t p r o d u c t i o n p r a c t i c e s and improved d a t a which become a v a i l a b l e f o r more exact a n a l y s i s , thus p e r m i t t i n g a c l o s e r approximation of the optimum o r d e r i n g p o l i c i e s . P r e f e r a b l y the d a t a p r o c e s s i n g f o r updating i n v e n t o r y l e v e l s , c a l c u l a t i n g m a t e r i a l requirements and determining order q u a n t i t i e s w i l l be done on a computer. The i n p u t s would then be m a t e r i a l withdrawals and r e c e i p t s on a semi-monthly b a s i s , and p r i c e and d e s i g n changes and p r o d u c t i o n schedules on a monthly b a s i s . A l l of t h i s d a t a would have to be put 119 i n t o a computer-acceptable form. The outputs would be c u r r e n t i n v e n t o r y l e v e l s , usage r a t e , m a t e r i a l c o s t , t o t a l m a t e r i a l requirements and r e o r d e r q u a n t i t i e s . The purchasing department would use the r e s u l t s , perhaps a d j u s t e d w i t h c o n s i d e r a t i o n of p r o s p e c t i v e s t r i k e s and other important random f a c t o r s , to p l a c e o r d e r s u s i n g the present c l e r i c a l procedure. These c o n s i d e r a t i o n s f o r implementing a t o t a l i n v e n t o r y c o n t r o l system suggest t h a t the c o s t s i n v o l v e d are a p p r e c i a b l e . The t a s k of i n c o r p o r a t i n g b i l l s of m a t e r i a l s i n t o a system f o r s p e c i f y i n g the m a t e r i a l requirements of p r o d u c t i o n schedules i s for m i d a b l e even u s i n g the matrix f o r m u l a t i o n . Considerable p r o f e s s i o n a l and c l e r i c a l time would be r e q u i r e d , perhaps as much as 1,000 hours. However, there are b e n e f i t s other than improved i n v e n t o r y c o n t r o l so t h a t not a l l of the c o s t s would be assigned to the i n v e n t o r y c o n t r o l system. Based on the experience of the author i n d e a l i n g w i t h the seven items t h a t were d i s c u s s e d above, the c o s t of f o r m u l a t i n g the remaining items has been s u b j e c t i v e l y approximated as |7,000 c o n s i d e r i n g the s t a f f and c o n s u l t a n t time i n v o l v e d . Programming the i n v e n t o r y c o n t r o l system would r e q u i r e approximately two months of a competent programmer's time and t h e r e f o r e would c o s t about #3,000. The present pur-chasing department s t a f f c o u l d probably handle the d a t a c o l l e c t i o n tasks but keypunching the d a t a would be an a d d i -120 t i o n a l o p e r a t i n g c o s t as would the e l e c t r o n i c d a t a p r o c e s s i n g . Again u s i n g past experience as a c r i t e r i o n , the c o s t would be i n the order of $500 per month. These rough estimates are l i s t e d i n Appendix I I I which i s a c a l c u l a t i o n of the net pre s e n t value of the i n v e n t o r y c o n t r o l system. F u r t h e r p r e l i m i n a r y d e s i g n of the system by a systems a n a l y s t would be necessary to r e f i n e these c o s t estimates. To assess the f e a s i b i l i t y of the system, some e s t i -mation of the b e n e f i t s i s a l s o necessary. The simulated use of OR formulated d e c i s i o n r u l e s f o r o r d e r i n g seven items of Company F's i n v e n t o r y has i n d i c a t e d s u b s t a n t i a l b e n e f i t s i n terms of reduced Inventory l e v e l s . These b e n e f i t s are e x t r a p o l a t e d f o r a one year p e r i o d and d i s p l a y e d i n terms of reduced i n v e n t o r y l e v e l s and o r d e r i n g , o u t - o f - s t o c k and c a r r y i n g c o s t s i n Table XI. The i n d i c a t e d seventy per cent r e d u c t i o n i n i n v e n t o r y i s somewhat m i s l e a d i n g . About one h a l f of the r e d u c t i o n i s accounted f o r by item D to which no o p p o r t u n i t y c o s t of funds can be a s s o c i a t e d because the Company i s not i n v o i c e d f o r i t u n t i l i t i s taken i n t o the p r o d u c t i o n p r o c e s s . A l s o these items tend to be among the most important to the Company i n terms of d o l l a r volume, r e p l a c e a b l l i t y and l e a d times. U n f o r t u n a t e l y , the p r o s p e c t i v e savings can not be used to a c c u r a t e l y estimate the s i m i l a r savings f o r the t o t a l i n v e n t o r y because the seven items do not r e p r e s e n t a TABLE XI COMPARISON OP RESULTS OP ACTUAL AND SIMULATED INVENTORY CONTROL A c t u a l Past Performance Item Average End-of-Month .Inventory L e v e l .-. C a r r y i n g Cost | . $/year. Ordering Cost $/year -T o t a l Cost . $/year A 925 1 3 5 45 180 B 3 , 5 0 0 5 2 0 25 545 C 5,200 780 3 0 810 D 33,040 480 2 5 5 0 5 2 , 2 5 0 337 1 6 353 F 7,270 1 , 0 9 0 48 1,138 G . 17,400 2 , 6 0 0 48 2,648. T o t a l s 69,585 5,942 2 3 7 6,179 1 2 1 Simulated Use of D e c i s i o n Rules Average C a r r y i n g Ordering Stock-out T o t a l P r o s p e c t i v e End-of-Month Cost Cost Cost Cost Y e a r l y Inventory L e v e l - $ 1 $/year $/year |/year |/year Saving-$/year 2 2 5 34 6 0 40 1 3 4 | 46 — — 2 5 0 2 5 $ 5 2 0 1 , 0 7 0 1 6 0 6 0 0 220 i 5 9 0 8,260 120 6 0 0 180 $ 3 2 5 4 5 0 68 5 6 0 124 1 2 2 9 2,240 3 3 6 1 3 2 0 468 i 6 7 0 8 , 7 0 0 r , 3 0 0 3 2 0 0 1,620 #1028 2 0 , 9 4 5 2,018 713 40 2,771 I3A08 random sample. A rough estimate based on the p r o p o r t i o n of high-valued i n v e n t o r y , and assuming savings of the same p r o p o r t i o n as f o r the seven items, I n d i c a t e s t h a t as much as $ 1 5 , 0 0 0 per year c o u l d be saved. In a d d i t i o n , implementation of a formal i n v e n t o r y c o n t r o l system would reduce the n e c e s s i t y of i n f o r m a l communications and as a consequence i n c r e a s e l a b o u r p r o d u c t i v i t y and reduce employee f r u s t r a t i o n . A l s o the accumulated d a t a would be u s e f u l f o r f u r t h e r im-pr o v i n g i n v e n t o r y c o n t r o l , f o r c o s t accounting and p r i c i n g , f o r p a r t s books and f o r o p e r a t i o n s r e s e a r c h i n r e l a t e d areas. The above d i s c u s s i o n has p r o v i d e d estimates, though v e r y rough, f o r e v a l u a t i n g the proposed i n v e n t o r y c o n t r o l system. Although the estimates are open to q u e s t i o n , the c a l c u l a t i o n of the net presen t v a l u e of i n c o r p o r a t i n g the i n v e n t o r y c o n t r o l system Is i n f o r m a t i v e f o r purposes of demonstrating a g e n e r a l approach to a s s e s s i n g the f e a s i b i l i t y of o p e r a t i o n s r e s e a r c h and systems d e s i g n and implementation. The c a l c u l a t i o n I s made i n Appendix I I I u s i n g a three year time h o r i z o n . Future net b e n e f i t s are di s c o u n t e d a t twelve per cent to g i v e a net presen t value of $ 9 , 5 0 0 . T h i s f i g u r e together w i t h the other b e n e f i t s a l r e a d y mentioned Is evidence t h a t o p e r a t i o n s r e s e a r c h coupled w i t h adequate i n f o r m a t i o n systems would be e f f e c t i v e as an a i d to i n v e n t o r y c o n t r o l i n t h i s s m a l l b u s i n e s s . 123, V. OPERATIONS RESEARCH IN OTHER AREAS Sales F o r e c a s t i n g S e c t i o n H I of t h i s chapter has o u t l i n e d problems i n other areas of the Company's o p e r a t i o n s . The problem of s a l e s f o r e c a s t i n g i s a l l p e r v a s i v e , p a r t i c u l a r l y a f f e c t i n g p r o d u c t i o n s c h e d u l i n g , i n v e n t o r y c o n t r o l and c a p i t a l budgeting. F o r e c a s t i n g f o r equipment purchases i s v i r t u a l l y i m p o s s i b l e because i t r e q u i r e s a t l e a s t a three year f o r e c a s t . However, the task of f o r e c a s t i n g f o r i n v e n t o r y c o n t r o l and p r o d u c t i o n s c h e d u l i n g i s not as imposing. In terms of the company's i n t e n t i o n to g r a d u a l l y convert to modular p r o d u c t i o n , s a l e s f o r e c a s t s are r e q u i r e d f o r determ i n i n g which and how many of each sub-assembly to b u i l d i n the succeeding two months. Without a c t u a l l y f o r m u l a t i n g a p r o d u c t i o n s c h e d u l i n g model, the r e q u i r e d p r o j e c t i o n time i s d i f f i c u l t to s p e c i f y . F o r e c a s t s f o r one year would c e r t a i n l y be s u f f i c i e n t f o r p r o d u c t i o n s c h e d u l i n g and i n v e n t o r y c o n t r o l . There i s some evidence t h a t economic f a c t o r s such as i n t e r e s t rates, c o u l d be used f o r p r e d i c t i n g the g e n e r a l l e v e l of demand. Past d a t a on these f a c t o r s c o u l d be used i n a r e g r e s s i o n a n a l y s i s to determine what e f f e c t they had on Company s a l e s . I f the r e g r e s s i o n c o e f f i c i e n t s were 1 2 % s t a t i s t i c a l l y s i g n i f i c a n t , the r e s u l t i n g equation c o u l d be used to f o r e c a s t an approximate l e v e l of demand. 1 1 T h i s c o u l d be a d j u s t e d by the s a l e s d i v i s i o n ' s assessment of market share, c l i e n t a t t i t u d e s and other f a c t o r s t h a t become known to them through t h e i r c o n t a c t s i n the market. T h i s type of f o r e c a s t i s not s u f f i c i e n t f o r p l a n n i n g purposes. An estimate of the equipment types and models t h a t w i l l be demanded must a l s o be made so as to determine the number of each sub-assembly that should be produced i n a g i v e n time p e r i o d . I n i t i a l l y , the s u b j e c t i v e o p i n i o n s of salesmen can be used f o r p r e d i c t i n g the d i s t r i b u t i o n o f s a l e s hy type and model but c a r e f u l a n a l y s i s of c l i e n t o p e r a t i n g needs may r e f i n e the estimate. The seasonal p a t t e r n o f demand i s a l s o necessary f o r p l a n n i n g . S t a t i s t i c a l a n a l y s i s of past s a l e s should be s u f f i c i e n t to i d e n t i f y the seasonal f a c t o r s i n demand. The a p p l i c a t i o n of o p e r a t i o n s r e s e a r c h to s a l e s f o r e -c a s t i n g i s a means of r e l a t i n g a l l of these f a c t o r s f o r f o r m u l a t i n g a comprehensive model which p r e d i c t s the g e n e r a l l e v e l of demand, the components of f o r e c a s t s a l e s and the seasonal v a r i a t i o n . Thus the s a l e s of machines by type and by month i s p r e d i c t e d so t h a t the sub-assembly requirements f o r a two month p e r i o d are obtained. The accuracy and thus the val u e of the model would be imp o s s i b l e to determine b e f o r e -hand. C e r t a i n l y export orders would produce c o n s i d e r a b l e C.C. H o l t , et. a l . P l anning P r o d u c t i o n , I n v e n t o r i e s  and Workforce. I960, pp. 145-151. 125 random v a r i a t i o n s . Even so, the v e r y l a r g e b e n e f i t s t h a t c o u l d be d e r i v e d from a c c u r a t e s a l e s f o r e c a s t i n g suggest t h a t c o n s i d e r a b l e e f f o r t should be expended i n an o p e r a t i o n s r e s e a r c h approach to t h i s problem. P r o d u c t i o n Scheduling The problem of p r o d u c t i o n s c h e d u l i n g breaks down i n t o s p e c i f y i n g completion dates and a l l o c a t i n g tasks between pro-d u c t i o n machines. With r e f e r e n c e to the problem of s p e c i f y i n g completion dates and g i v e n t h a t s a l e s do f l u c t u a t e , there e x i s t s s e p a r a t e l y or i n combination a l i m i t e d number of a l t e r -n a t i v e courses of a c t i o n . L i s t i n g them s e p a r a t e l y , they a r e : 1) m a i n t a i n f i n i s h e d goods i n v e n t o r y , 2) backorder d u r i n g p e r i o d s of peak demand, 3) h i r e and l a y - o f f workers as r e q u i r e d , k) m a i n t a i n a f u l l p r o d u c t i o n complement while v a r y i n g p r o -d u c t i o n r a t e or 5) use overtime l a b o u r d u r i n g peak demand. As suggested before the problem i s to determine which a l t e r n a t i v e or, more l i k e l y , which combination of a l t e r n a t i v e s p r o v i d e s the minimum c o s t o p e r a t i o n f o r a g i v e n s a l e s f o r e c a s t . In t h i s r e g a r d c o n s i d e r a b l e i n v e s t i g a t i o n i s necessary to o b t a i n the r e l e v a n t c o s t s . For i n s t a n c e , the c o s t of main-t a i n i n g f i n i s h e d goods i n i n v e n t o r y i n c l u d i n g the p o s s i b i l i t y of obselescence must be determined. A number of methods have been formulated f o r s o l v i n g t h i s type of problem. A s e r i e s of models based on the l i n e a r 12)6 d e c i s i o n r u l e s o f Ho l t , et a l . have been d e v e l o p e d . 1 2 ' » 1 ^ L i n e a r programming can a l s o be used f o r t h i s type of problem. 1^ No doubt there are other OR techniques t h a t c o u l d be a p p l i e d but to determine which of these models i s most s u i t a b l e f o r t h i s s i t u a t i o n would r e q u i r e c o n s i d e r a b l e a n a l y s i s and i s beyond the scope of t h i s t h e s i s . The aspect of a l l o c a t i n g t asks to p r o d u c t i o n machinery co u l d be i n c o r p o r a t e d i n t o a l i n e a r programming or s i m u l a t i o n model which i s a l s o used f o r s c h e d u l i n g completion dates. Such a model would be complex and expensive to formulate. Rather, i t i s recommended t h a t a s m a l l s i m u l a t i o n model c o u l d be formulated to t e s t v a r i o u s s t r a t e g i e s . Only machines which can do s i m i l a r t a s k s , would be i n c o r p o r a t e d . Perhaps even more b e n e f i t would accrue from doing economic l o t s i z e a n a l y s i s f o r major p a r t s w i t h r e l a t i v e l y h i g h usage r a t e s such as item B i n the "Inventory Study". C a p i t a l Budgeting The problem of deter m i n i n g the p r o d u c t i o n equipment 1 2 H o l t e t a l , op_. c i t . pp. 4 7 - 6 3 •^E.H. Bowman, "Consistency and Optimal!ty i n Managerial D e c i s i o n Making" ( 1 9 6 6 ) pp. 4 7 9 - 4 9 2 . l i +E.S. Buff a, "Aggregate Planning f o r P r o d u c t i o n " ( 1 9 6 7 ) , P P . 8 7 - 9 7 . 15E.H. Bowman, "Production Scheduling by the Trans-p o r t a t i o n Method of L i n e a r Programming" ( 1 9 6 6 ) pp. 4 7 5 - ^ 7 9 . 127 to buy so as to o b t a i n a h i g h r e t u r n on investment while p r o v i d i n g f o r r a p i d growth i s extremely complex. Wot o n l y are t h e r e hundreds of a l t e r n a t i v e s but a l s o an assessment of f u t u r e requirements i s n e a r l y i m p o s s i b l e . The l a r g e v a r i e t y of p a r t s r e q u i r e d and the e q u a l l y l a r g e number of machine t o o l s a v a i l a b l e g i v e r i s e to the m u l t i t u d i n o u s a l t e r n a t i v e s . The r a p i d i t y of t e c h n o l o g i c a l change and the h i g h l y f l u c t u a t i n g demand f o r the Company's products g i v e r i s e to the d i f f i c u l t i e s i n d e termining f u t u r e requirements. In s p i t e of the complexity of the problem, the d e c i -s i o n s must be made e i t h e r by 'seat-of-the-pants" or v a r y i n g degrees of a n a l y s i s . The task of e v a l u a t i n g a l l p o s s i b l e a l t e r n a t i v e s to o b t a i n r a t e s of r e t u r n f o r each i s not f e a s i b l e p a r t i c u l a r l y because of the i n t e r a c t i n g nature of the a l t e r n a t i v e s . Perhaps a s i m u l a t i o n model co u l d be formu-l a t e d but a t t h i s p o i n t i t i s d i f f i c u l t to envisage a w o r r k — able model. A l i n e a r programming model c o u l d be formulated f o r s e l e c t i n g the best combination of p r o d u c t i o n machines. In t h i s model, the independent v a r i a b l e s would be hours of machine time, the c o n s t r a i n t equations would be based on the p r o d u c t i o n requirements and the c o e f f i c i e n t s i n the o b j e c t i v e equation would be the charge-out r a t e s which would be necessary to g i v e an adequate r a t e of r e t u r n on the c a p i t a l Invested i n each machine. These pr o p o s a l s may not be p r a c t i c a l but the complexity of the task and i t s importance to the Company's go a l s i n d i c a t e t h a t c o n s i d e r a b l e o p e r a t i o n s a n a l y s i s Is war-rante d In the area of c a p i t a l budgeting. CHAPTER VI SUMMARY AND CONCLUSIONS T h i s study was undertaken to determine the p r a c t i -c a b i l i t y of u s i n g o p e r a t i o n s r e s e a r c h i n small b u s i n e s s . In the study o p e r a t i o n s r e s e a r c h i s con s i d e r e d to be a separate management f u n c t i o n i n p a r a l l e l r e l a t i o n s h i p w i t h systems a n a l y s i s , i n d u s t r i a l e n g i n e e r i n g and ot h e r s and i s d e f i n e d as r e s e a r c h on the o p e r a t i o n s of g o a l - d i r e c t e d o r g a n i z a t i o n s . For purposes of t h i s study a busi n e s s i s con s i d e r e d to be s m a l l I f the volume of i t s business as measured by va l u e added Is l e s s than f i v e m i l l i o n d o l l a r s per year. The prevalence and e f f e c t i v e n e s s of OR i n i n d u s t r y and the management needs of smal l businesses were examined to determine whether o p e r a t i o n s r e s e a r c h should be used as a small business management a i d . A number of surveys on the use of o p e r a t i o n s r e s e a r c h i n the United S t a t e s , Canada and B r i t a i n i n d i c a t e t h a t OR i s used by a s i g n i f i c a n t , and growing p r o p o r t i o n of l a r g e companies, t h a t i t i s p r o v i n g to be an e f f e c t i v e a i d to management and t h a t r a t h e r few small companies use OR. On the other hand causes of small business f a i l u r e s and p u b l i s h e d r e s e a r c h i n d i c a t e t h a t s m a l l business management Is weak i n areas where o p e r a t i o n s 129 r e s e a r c h can be a p p l i e d . A survey of l o c a l s m a l l businesses was conducted by the author to assess the extent to which o p e r a t i o n s r e s e a r c h i s used i n small b u s i n e s s , to determine management's f a m i l i a r i t y w i t h o p e r a t i o n s r e s e a r c h and to i d e n t i f y the reasons why i t i s not used more e x t e n s i v e l y . Managers of twelve f i r m s were p e r s o n a l l y questioned a c c o r d i n g to a standard format. By and l a r g e the managers d i s p l a y e d c o n s i d e r a b l e i n t e r e s t as evidenced by the l e n g t h o f the d i s c u s s i o n s which c a r r i e d on f o r as much as three hours and never l e s s than one hour i n each case. As a r e s u l t , the author gained c o n s i d e r a b l e i n s i g h t as to the a t t i t u d e s of s m a l l business managers, the reasons f o r non-use of o p e r a t i o n s r e s e a r c h and the o p e r a t i n g problems of s m a l l b u s i n e s s . T h i s survey, a survey on the use of modern management techniques by s m a l l businesses i n the A t l a n t i c p r o v i n c e s and c o n v e r s a t i o n s w i t h c o n s u l t a n t s and o t h e r s d e a l i n g w i t h s m a l l business management problems have pr o v i d e d c o n s i d e r a b l e evidence t h a t o p e r a t i o n s r e s e a r c h i s used to a r a t h e r l i m i t e d extent by small businesses g e n e r a l l y . In the present survey, f o u r out of twelve companies had used OR but then o n l y as a p p l i e d to one or two s p e c i f i c problems and not as a g e n e r a l a c t i v i t y . However, OR has proved e f f e c t i v e i n v i r t u a l l y a l l i n s t a n c e s where i t has been a p p l i e d by companies i n the survey and by other s m a l l businesses as r e p o r t e d i n the l i t e r a t u r e . The survey and r e s e a r c h sponsored by the United S t a t e s Small Business A d m i n i s t r a t i o n have i d e n t i f i e d the f o l l o w i n g as 130 reasons why o p e r a t i o n s r e s e a r c h Is not used more e x t e n s i v e l y by s m a l l b u s i n e s s : 1) The n o n - a n a l y t i c a l approach of management to o p e r a t i n g problems, 2) Management's l a c k of f a m i l i a r i t y w i t h OR, 3) The l a c k of smal l business personnel who are capable of doing o p e r a t i o n s a n a l y s i s , k) The u n a v a i l a b i l i t y of accurate, r e l e v a n t data, 5) The c o s t and a v a i l a b i l i t y of e l e c t r o n i c computers, 6) Managements' a p p r a i s a l t h a t c o s t s are h i g h and b e n e f i t s s m a l l i n u s i n g OR. To v a r y i n g degrees the above reasons are r e l e v a n t to l a r g e companies but t h i s study i n d i c a t e s t h a t they are more p r e v a l e n t In s m a l l b u s i n e s s e s . The survey confirmed the e x i s t e n c e of problems to which o p e r a t i o n s r e s e a r c h might w e l l be a p p l i e d . Inventory c o n t r o l , p r o d u c t i o n s c h e d u l i n g and c a p i t a l budgeting were i d e n t i f i e d as major areas i n which problems e x i s t t h a t might be e f f e c t i v e l y s olved by the a p p l i c a t i o n of o p e r a t i o n s r e s e a r c h . The Small Business A d m i n i s t r a t i o n sponsored r e s e a r c h has i n d i c a t e d other problems, such as job c o s t e s t i m a t i n g which c o u l d be sol v e d by the use of OR. The employment of c o n s u l t a n t s and the a v a i l a b i l i t y o f inexpensive e l e c t r o n i c d a t a p r o c e s s i n g were examined as means of overcoming the l a c k of t r a i n e d a n a l y s t s and the hig h c o s t of l e a s i n g and o p e r a t i n g computers both of which are hindrances 131 to the use of OR i n small b u s i n e s s . The h i g h c o s t of r e t a i n i n g q u a l i f i e d c o n s u l t a n t s tends to overshadow the obvious b e n e f i t s of t h e i r s e r v i c e s . Examination of the reasons f o r the h i g h c o s t of c o n s u l t a n t ' s s e r v i c e s suggests t h a t they can be more e f f e c t i v e l y r e t a i n e d f o r a p p l y i n g o p e r a t i o n s r e s e a r c h to a s m a l l business under the f o l l o w i n g c o n d i t i o n s : 1) The c o n s u l t a n t maintains a c o n t i n u i n g r e l a t i o n s h i p w i t h the s m a l l business and i s able to o f f e r a s s i s t a n c e i n other f u n c t i o n a l areas. 2) The c o n s u l t a n t has a s m a l l and f l e x i b l e o p e r a t i o n which uses the s e r v i c e s of other q u a l i f i e d persons i n p e r i o d s of peak a c t i v i t y . Computer s e r v i c e bureaus, computer ti m e - s h a r i n g s e r v i c e s and s m a l l , l e a s e d computers are d i s c u s s e d f o r purposes of i d e n t i f y i n g t h e i r s u i t a b i l i t y as t o o l s i n f o r m u l a t i n g and imple-menting o p e r a t i o n s r e s e a r c h i n a s m a l l b u s i n e s s . Small computers are f a i r l y expensive i n terms of r e n t a l and o p e r a t i n g c o s t s and t h e r e f o r e they are o n l y f e a s i b l e i f the small business has many other EDP jobs b e s i d e s o p e r a t i o n s r e s e a r c h . A l s o , they may not be capable of e f f i c i e n t l y h a n d l i n g the l a r g e models which might be formulated i n the course of o p e r a t i o n s r e s e a r c h a c t i v i t i e s . The t i m e - s h a r i n g s e r v i c e i s an economical and f l e x i b l e t o o l f o r o b t a i n i n g s o l u t i o n s to c a p i t a l budgets, l i n e a r programmes and other OR techniques of l i m i t e d s i z e . M a i n t a i n i n g p r o p r i e t a r y 132 programmes and d a t a o n - l i n e i n d i s c storage a t t i m e - s h a r i n g f a c i l i t i e s may be warranted f o r ease of updating and ac-c e s s i n g d a t a f i l e s and f o r q u i c k d e c i s i o n making such as c a l c u l a t i n g a r e o r d e r q u a n t i t y . T h i s s e r v i c e w i l l become i n c r e a s i n g l y a t t r a c t i v e w i t h the development of computers w i t h even g r e a t e r c a p a b i l i t i e s but w i l l be l i m i t e d i n remote areas by the r e l a t i v e l y h i g h c o s t of communication l i n e s ; For p e r i o d i c batch p r o c e s s i n g of computer programmes based on o p e r a t i o n s a n a l y s i s , the computer s e r v i c e bureaus o f f e r an i n e x p e n s i v e s e r v i c e . The preceeding summary has i n d i c a t e d t h a t i n g e n e r a l o p e r a t i o n s r e s e a r c h might w e l l be a p p l i e d to s m a l l business management problems and t h a t i n p a r t i c u l a r i t has been s u c c e s s f u l l y a p p l i e d i n a number of cases. The reasons which up to the present have l i m i t e d the use of o p e r a t i o n s r e s e a r c h i n s m a l l b u s i n e s s have been i d e n t i f i e d and suggestions g i v e n f o r overcoming these hindrances. However, the p r a c t i c a b i l i t y of u s i n g OR i n s m a l l business can o n l y be determined i n a p a r t i c u l a r s i t u a t i o n . To t h i s end a case study of a l o c a l s m a l l company was made to i d e n t i f y problems to which e f f e c -t i v e s o l u t i o n s might be found through o p e r a t i o n s a n a l y s i s and to assess the value of o p e r a t i o n s r e s e a r c h as a p p l i e d to one of the problems. 133 Many hours were spent w i t h the Company's e x e c u t i v e s i n d i s c u s s i n g the business, o r g a n i z a t i o n and o p e r a t i o n s of the Company and i n i d e n t i f y i n g major o p e r a t i n g problems. The main o b j e c t i v e of the Company i s r a p i d growth w i t h an adequate p r o f i t on s a l e s as a manufacturer of heavy equipment which i s used i n one phase o f a majjor Canadian i n d u s t r y . Problems i n the areas of s a l e s f o r e c a s t i n g , c a p i t a l budgeting, p r o d u c t i o n s c h e d u l i n g and i n v e n t o r y c o n t r o l were noted as being c o n s t r a i n t s to the s u c c e s s f u l attainment of the company's o b j e c t i v e s . Inventory c o n t r o l was s e l e c t e d as an a r e a to i l l u s t r a t e o p e r a t i o n s r e s e a r c h as a p p l i e d to a s m a l l b u s i n e s s . The r e l e v a n t c h a r a c t e r i s t i c s of the Company's i n v e n t o r y were d e t e r -mined i n d i s c u s s i o n s w i t h purchasing department personnel and by examination of i n v e n t o r y r e c o r d s , b i l l s o f m a t e r i a l and other data. The l a c k of e x p l i c i t l y s t a t e d i n f o r m a t i o n on stock l e v e l s and m a t e r i a l requirements were i d e n t i f i e d as c o n s t r a i n t s to the e f f e c t i v e c o n t r o l of I n v e n t o r i e s . The wide v a r i e t y of items i n terms of s u p p l i e r p o l i c i e s , v a l u e , demand c h a r a c t e r -i s t i c s and p l a n t p r o d u c t i o n p r a c t i c e e l i m i n a t e d the p o s s i b i l i t y of u s i n g a s m a l l random sample as a b a s i s f o r determining the value of an o p e r a t i o n s r e s e a r c h based i n v e n t o r y c o n t r o l system. As an a l t e r n a t i v e seven important and r e p r e s e n t a t i v e items were s e l e c t e d as the b a s i s f o r proposing and e v a l u a t i n g ao periodic;. Inventory c o n t r o l system. The r a t h e r unusual and v a r i e d c h a r a c t e r i s t i c s of these items made i t i m p o s s i b l e to use any one standard textbook technique f o r f o r m u l a t i n g the o r d e r i n g d e c i s i o n r u l e s . The standard economic order q u a n t i t y formula was used to d e t e r -mine the frequency of orders r e c o g n i z i n g t h a t c e r t a i n con-s i d e r a t i o n s suggested a g a i n s t o r d e r i n g more f r e q u e n t l y than twice a month. The concept of d e c i s i o n t a b l e s was adapted f o r d e t e r m i n i n g the q u a n t i t y of r e s e r v e stock which would r e s u l t i n the lowest expected i n v e n t o r y c o s t s . In t h i s regard, s u b j e c t i v e p r o b a b i l i t y d i s t r i b u t i o n s were obtained from the Company's managers f o r determining the expected o u t - o f - s t o c k c o s t f o r each item. Thus the author used a r a t h e r unique o v e r a l l approach to f o r m u l a t i n g o r d e r i n g p o l i c i e s f o r each of the seven items. The o r d e r i n g d e c i s i o n r u l e s were then used i n s i m u l a -t i o n s of past experience to estimate improvements i n opera-t i o n s as compared to a c t u a l performance. The estimated gross b e n e f i t s f o r seven items would have been $3400 i f the d e c i s i o n r u l e s had been used f o r a r e c e n t one year p e r i o d . C o n s i d e r a t i o n of the requirements of an i n v e n t o r y c o n t r o l system u s i n g o r d e r i n g r u l e s based on o p e r a t i o n s r e s e a r c h f o r a l l important items p r o v i d e d a b a s i s f o r making rough estimates of the c o s t of f o r m u l a t i n g , implementing and 135 o p e r a t i n g the system. These c o s t s together w i t h a p r o j e c t i o n f o r three years of the p r o s p e c t i v e economic b e n e f i t s i n d i c a t e d t h a t the system had a net present value of $9500 u s i n g twelve per cent as an estimate o f the f i r m ' s c o s t of c a p i t a l . The economic and other b e n e f i t s of t h i s proposed system are evidence o f the p r a c t i c a b i l i t y of u s i n g o p e r a t i o n s r e s e a r c h i n s m a l l b u s i n e s s . Subsequently, suggestions were made f o r a p p l y i n g OR i n the areas of s a l e s f o r e c a s t i n g , p r o d u c t i o n s c h e d u l i n g and c a p i t a l budgeting. In c o n c l u s i o n , the study has pr o v i d e d c o n s i d e r a b l e evidence to support the three p r o p o s i t i o n s i n the T h e s i s Statement. 1 That o p e r a t i o n s r e s e a r c h i s r a r e l y used i n smal l b u s i n e s s was i n d i c a t e d by the author's survey of l o c a l s m a l l companies and by other r e p o r t e d surveys. The study a l s o i n d i -c a t e d t h a t o p e r a t i o n s r e s e a r c h i s used to a r a t h e r l i m i t e d extent i n s m a l l b u s i n e s s e s because of management's l a c k of f a m i l i a r i t y w i t h OR and because of the l a c k of small business p e r s o n n e l who are capable of doing the o p e r a t i o n s a n a l y s i s ; although the survey and other r e s e a r c h i d e n t i f i e d a d d i t i o n a l reasons f o r non-use. F i n a l l y , many problems to which OR can be a p p l i e d e x i s t i n smal l b u s i n e s s ; o p e r a t i o n s r e s e a r c h has gener-a l l y been e f f e c t i v e when a p p l i e d to small business problems, the e f f e c t i v e n e s s of OR has been i l l u s t r a t e d i n a case study; and many of the reasons f o r not u s i n g o p e r a t i o n s r e s e a r c h i n See page 1 136 s m a l l business can be overcome. These statements, which are based on the f i n d i n g s of t h i s study, support the p r o p o s i t i o n t h a t o p e r a t i o n s r e s e a r c h c o u l d be used more e x t e n s i v e l y as an e f f e c t i v e a i d i n the management of smal l b u s i n e s s . 137 BIBLIOGRAPHY A. OPERATIONS RESEARCH DEFINITIONS, METHODS, SURVEYS Ackoff, R.L. (ed.). "The Meaning, Scope and Methods of Operations Research," Progress i n Operations Research, V o l . I, New York, John Wiley and Sons, 1961. pp. 1-34. Beer, S t a f f o r d . "Cybernetics and O p e r a t i o n a l Research." O p e r a t i o n a l Research Q u a r t e r l y , V o l . 10 (1959). pp. 1-21. Bevan, R.W. "Trends i n O p e r a t i o n a l Research." Operations  Research, V o l . 6 (1958), pp. 441-447. Bowman, E.H. "Production Scheduling by the T r a n s p o r t a t i o n Method of L i n e a r Programming." Readings i n Prod u c t i o n  and Operations Management, ed. E.S. B u f f a . Sydney, John Wiley and Sons, l " o 6 . pp. 475-498. . "Consistency and O p t i m a l l t y i n Managerial D e c i s i o n Making," i n Readings i n Pr o d u c t i o n and Operations Man-agement , ed. E.S. B u f f a . Sydney, John Wiley and Sons, 1966, pp. 479-492. Brown, R.G. S t a t i s t i c a l F o r e c a s t i n g f o r Inventory C o n t r o l . New York, McGraw-Hill, 1959. B u f f a , E.S. "Aggregate P l a n n i n g f o r P r o d u c t i o n . " Business  Horizons, V o l . 10, No. 3 ( F a l l 1967), pp. 87-97. Churchman, C.W. "A Survey o f Operations Research Accomplish-ment i n I n d u s t r y . " Proceedings of the Conference on  'What i s Operations Research Accomplishing i n Industry', Ceveland, Case I n s t i t u t e of Technology, 1955. Fabrycky,. W.I. and Torgenson, P.E. Operations Economy: I n d u s t r i a l A p p l i c a t i o n s of Operations Research, Englewood C l i f f s , N.J., P r e n t i c e H a l l , 1966. F e r r e r o d i R o c c a f e r r e r a , G.M. Operations Research Models f o r Business and Industry. Chicago, South-Western Pub-l i s h i n g , 1964", 1 3 8 Gander, R.S. "The. State, of. O p e r a t i o n a l Research i n the United Kingdom. Proceedings of the F i r s t I n t e r n a t i o n a l Con- fer e n c e on Operations Research, Baltimore Operations Research S o c i e t y of America, 1 9 5 7 . PP. 5 0 0 - 5 1 3 . Goodeve, C.F. . "The S c i e n t i f i c Method". . Proceedings of the F i r s t I n t e r n a t i o n a l Conference on Operations Research, Baltimore, ORSA, 1 9 5 7 , PP. 9 - 1 9 . Herrman, C.C. and Magee ..J.F. "Operations Research f o r Manage-ment ." S c i e n t i f i c D e c i s i o n Making i n Business, ed. A. Schuchman, New York, H o l t , R i n e h a r t and Winston, 1 9 6 3 . Hertz, D.B. "Progress of I n d u s t r i a l Operations. Research .in the U.S." Proceedings o f the F i r s t I n t e r n a t i o n a l Con-fer e n c e on Operations Research, Baltimore, ORSA, 1 9 5 7 , pp. 4 5 5 - 4 6 8 . H o l t , C.C... e t a l . Planning P r o d u c t i o n , I n v e n t o r i e s and Work  Force. Englewood C l i f f s , N.J. P r e n t i c e H a l l , 1962. Jessop, W.N... . ."Operational Research Methods, What are They?" O p e r a t i o n a l Research Q u a r t e r l y , V o l . 7 ( 1 9 5 6 ) , pp. 4 9 - 5 8 . Lieberman, I . J . "A Mathematical Model f o r I n t e g r a t e d Business Systems." Management Science, V o l . 2 , No. 4 ( J u l y , 1 9 5 6 ) , P P . 3 2 7 - 3 3 6 . M i l l e r , D.W., and S t a r r , M.K. E x e c u t i v e D e c i s i o n s and Operations Research. Englewood C l i f f s , N.J., P r e n t i c e H a l l , I960. O ' R e i l l y , F.J.. . ."Why Operations Research Doesn't Always Work". Management Review, V o l . 5 6 (Apr. 1 9 6 7 ) , pp. 5 3 - 5 6 . R i v e t t , B.H.P. "A Survey of O p e r a t i o n a l Research i n B r i t i s h I n d u s t r y . " O p e r a t i o n a l Research Q u a r t e r l y , V o l . 1 0 ( 1 9 5 9 ) , PP. 1 8 9 - 2 0 5 . Robinson, P..J. "Op e r a t i o n a l Research, i n Canada. " Proceedings  of the F i r s t I n t e r n a t i o n a l Conference on Operations  Research. Baltimore, ORSA, 1957, pp. 469-490. Schumacher, C.C. and Smith, B.E. "Sample Survey of I n d u s t r i a l Operations Research A c t i v i t i e s . " Operations Research, V o l . 1 3 ( 1 9 6 5 ) , PP. 1 0 2 3 - 1 0 2 7 . 139 Solandt, 0 , "Observation, Experiment, and Measurement i n Operations Research," J o u r n a l Operations Research  S o c i e t y of America, V o l . 7, (1955). PP. 1-14. S t a r r , M.K. and M i l l e r , D.W. Inventory C o n t r o l : Theory and  Practice'. Englewood C l i f f s , N.J., P r e n t i c e H a l l , 1962. Swan, A.W... "The Name and Nature of OR." O p e r a t i o n a l Research  Q u a r t e r l y , V o l . 8 (1957), PP. 1-5. V a t t e r , W.J. "The Use. of Operations. Research i n American Companies." The Accounting Review, V o l . 42, No. 4 (Oct. 1967), PP. 721 -730. B, MANAGEMENT OP SMALL BUSINESS A l l e n , L.A. "Where Small Business Goes Wrong." Dun's Review, (May 1 9 6 5 ) , PP. 6 0 , 6 1 , 117-124. Bostrom,. K.. "The Role. of. Small Businesses i n a Dynamic S o c i e t y . " Advanced Management J o u r n a l , V o l . 31 (Jan. 1 9 6 6 ) , pp. 1 6 - 2 0 . Broom, H.N. and Longenecker, J.G. Small Business Management. Chicago, South-Western P u b l i s h i n g , 1966 . Canada, 1 9 6 4 —Report of the Royal Commission on Banking and  Finance. Ottawa. Queen's P r i n t e r . 1964. pp. 4 3 - 4 6 . Dewhurst, G.H. The Small Business Loan Act.. MBA T h e s i s , U n i v e r s i t y of B.C., 1967. "A Future f o r Small B u s i n e s s . " Business Week, ( J u l y 3 1 , 1 9 6 5 ) , PP. 3 5 , 3 6 , 3 8 . Hoad, W.M. and Rasko, P. Management F a c t o r s C o n t r i b u t i n g to  the Success or F a i l u r e of New Small Manufacturers. Ann Arbor, Michigan, Bureau of Business Research, U n i v e r s i t y of Michigan, 1964 . Krentzman, H.C. and Samaras, J.N. "Can Small Businesses Use C o n s u l t a n t s ? " Harvard Business Review, V o l . 38 , No. 3 (May-June i 9 6 0 ) , pp. 126-136. Puf f , H.F... . "Problems, and P r a c t i c e s of the Small Manufacturer," Advanced Management, V o l . 1, No. 5 (June, 1 9 6 2 ) , PP. 3 3 - 3 4 . 140 S t e k l e r , H.O. " P r o f i t a b i l i t y and S i z e of Fi r m . " Washington, U.S. Small Business A d m i n i s t r a t i o n , 1963 . (Management Research Summary No. 1 3 1 , 5 - 6 3 . ) "Why New Businesses Succeed." Nation's Business, V o l . 52 (Apr. 1 9 6 4 ) , pp. 56,57,58. Witschey,. R.E. "Management Problems of Small B u s i n e s s . " J o u r n a l of Accountancy, V o l . 114, No. 2 (Aug. 1 9 6 2 ) . Wildgen, F.X. F i n a n c i n g Small Business. A. study prepared f o r the 1964 Royal Commission on Banking and Finance. Unpublished d r a f t . ( 1 9 6 2 ) . Woodruff, A.M.. .and Alexander, T.G. Success and F a i l u r e i n Small Manufacturing. P i t t s b u r g h , U n i v e r s i t y of P i t t s -burgh Press, 1958 . Worthy, J.C. "Who F a i l s and Why?" Advanced Management J o u r n a l , V o l . 31 (Jan. 1966) pp. 2 1 - 2 6 . Wyant, Rowena, "Business F a i l u r e s " . Dun's Review, March 1968 , pp. 1 1 9 - 1 2 0 . C. COMPUTERS FOR SMALL BUSINESS Bergwerk, R.J. "Data P r o c e s s i n g f o r Small B u s i n e s s . " J o u r n a l of Accountancy, V o l . 116 , No. 6 (Dec. 1 9 6 3 ) , PP. 5 1 - 5 4 . Brown, R.R. "Cost and Advantages of On-line DP." Datamation, V o l . 14, No. 3 (March 1 9 6 8 ) , pp. 40 - 4 3 . Finke, W.W.. "Computers, Yesterday,. Today and Tomorrow." C r e d i t and F i n a n c i a l Management, V o l . 68 , No. 1 (Jan. 1 9 6 6 ) , pp. 18 - 2 0 . : Irwin, M.R.. "Small Business and Time-Shared. Computer System". Q u a r t e r l y Review of Economics & Business, V o l . 7 (Spring 1 9 6 7 ; , PP. 2 1 - 2 9 . ; 1 Ruskin, V.W. Computer User F a c t s 1 9 6 7 / 6 8 : P a r t I - Canada. Vancouver, Mechanical E n g i n e e r i n g Department, U n i v e r s i t y of B r i t i s h Columbia, 1968 . S e l i g s o n , I . J . Using Computer S e r v i c e s i n Small Businesses, Washington, United States Small Business A d m i n i s t r a t i o n , 1962 . (Management Aids f o r Small Manufacturers, No. 8, pp. 82 - 8 6 . ) 141 Watson, E...J. .."Computer S e r v i c e s f o r Small B u s i n e s s e s . " Management Accounting, V o l . 4 7 , No. 2 (Oct. 1 9 6 5 ) . p p . 1 1 - 1 3 . D. OPERATIONS RESEARCH FOR SMALL BUSINESS Axelson,. K.S. "Examples, of Operations Research A p p l i c a t i o n s , " J o u r n a l of Accountancy, V o l . I l 4 , No. 6 (Dec. 1 9 6 2 ) , P P . 7 7 - 7 9 . Baum, H.L. J r . "The Use of Operations Research i n a Small Company." Operations Research Reconsidered, New York, Finance D i v i s i o n , American Management A s s o c i a t i o n , 1 9 5 7 . Fowler, P.P.. and.Sandberg, E.W. The R e l a t i o n s h i p of. Manage- ment Decision-Making to Small Business Growth. Colorado State U n i v e r s i t y Research Foundation, 1964. Freedman, H.S. " S c i e n t i f i c Management i n Small B u s i n e s s e s . " Harvard Business Review, V o l . 2 8 , No. 3 (May 1 9 5 0 ) , P P . 3 3 - 5 3 . Gavett, W.J. and A l l d e r i d g e , J.M. Operations A n a l y s i s i n Small Manufacturing Firms." Washington, United States Small Business A d m i n i s t r a t i o n , 1 9 6 3 . (Management Research Summary 9 7 - 2 - 6 3 ) . Holdren, B.R. e t a l . Operations Research i n Small B u s i n e s s : A Case Study. Iowa C i t y , Bureau of Business and Economic Research, U n i v e r s i t y of Iowa, 1 9 6 3 . Hosford, J.E. Operations Research f o r Small Business. Washington, United States Small Business A d m i n i s t r a t i o n , 1964, ( T e c h n i c a l Aids f o r Small Manufacturers, No. 8 7 ) . Lavoie, J.C. e t a l . "Management Concepts and Methods i n the Smaller Company". A Paper Prepared f o r the Conference, " P r o d u c t i v i t y Through New Technology" - H a l i f a x , Oct. 24 -2 5 , 1966. 142 APPENDIX I QUESTIONNAIRE USED IN SURVEY OF LOCAL SMALL BUSINESSES The author made appointments w i t h managers of l o c a l s m a l l businesses to o b t a i n answers to the f o l l o w i n g q u e s t i o n -n a i r e . Many of the qu e s t i o n s , p a r t i c u l a r l y as to the f e a s i -b i l i t y of u s i n g OR, c o u l d o n l y be answered i n many cases a f t e r c o n s i d e r a b l e e x p l a n a t i o n by the author. Thus the n e c e s s i t y o f the i n t e r v i e w technique. The q u e s t i o n s asked by the i n t e r v i e w e r are l i s t e d as f olloxtfs: 1) What i s the s i z e of t h i s b u s i n e s s i n terms of number of employees and va l u e added (or s a l e s revenue i f va l u e added i s not a v a i l a b l e ) ? 2) How many p r o f e s s i o n a l s (or u n i v e r s i t y graduates and t e c h n o l o g i s t s does t h i s f i r m employ? 3) Has t h i s f i r m ever obtained the s e r v i c e s o f management c o n s u l t a n t s ? 4) Is the management of t h i s company f a m i l i a r w i t h the f o l l o w i n g terms? - Operations Research - C r i t i c a l ' P a t h Methods - Inventory C o n t r o l - Economic Order Q u a n t i t i e s - Mathematical Programming 143 - S i m u l a t i o n - C a p i t a l Budgeting Depending on the knowledge d i s p l a y e d by the manager, the author gave b r i e f e x p l a n a t i o n s of the above terms p a r t i c u l a r l y emphasizing o p e r a t i o n s r e s e a r c h . 5 ) Has any member of the management team of t h i s f i r m ever used OR i n s o l v i n g a p a r t i c u l a r problem? A) The f o l l o w i n g q u e s t i o n s are f o r those who answered # 5 i n the a f f i r m a t i v e . A6) In the management's o p i n i o n were the r e s u l t s e f f e c t i v e ? Can you (the e x e c u t i v e ) g i v e concrete r e s u l t s ? A7) I f the r e s u l t s were not e f f e c t i v e , what were the main causes or d o w n f a l l s ? A8) Is o p e r a t i o n s r e s e a r c h being used on a r e g u l a r b a s i s ? - i n which a r e a ( s ) ? A 9 ) Are there any p l a n s to broaden the use of o p e r a t i o n s r e s e a r c h i n t h i s b u s i n e s s ? Are there problems i n t h i s b u s i n e s s which OR might e f f e c t i v e l y s o l v e ? A10) G e n e r a l l y , to what extent does the OR a p p l i e d i n t h i s b usiness reap b e n e f i t s i n excess of c o s t s ? A l l ) What are the c o n s t r a i n t s on the i n c r e a s e d use of OR i n t h i s b u s i n e s s ? (eg. s u i t a b l e problems, t r a i n e d personnel, d a t a a v a i l a b i l i t y , dynamic changes i n the environment.) B) Questions to be answered by those who responded to # 5 i n the n e g a t i v e . 144 B6) Has management ever c o n s i d e r e d the use of op e r a t i o n s r e s e a r c h to improve o p e r a t i n g e f f i c i e n c y ? I f not, why not? (eg. u n f a m i l i a r i t y , l a c k o f t r a i n e d personnel, l a c k of s u i t a b l e problems, d a t a a v a i l a b i l i t y ? ) B7) What are the main problems i n managing t h i s b usiness to which no s a t i s f a c t o r y s o l u t i o n has been obtained? Would s o l u t i o n of these problems r e s u l t i n i n c r e a s e d p r o f i t s ? B8) Does the ex e c u t i v e c o n s i d e r t h a t OR might be u s e f u l l y a p p l i e d to f i n d a s o l u t i o n to these problems? 145 APPENDIX II GENERATING MATERIAL REQUIREMENTS USING A MATRIX FORMULATION A materials 'explosion* system has many similar properties to a business information system as perceived by Lieberman. Just as there are various reporting l e v e l s In a business information system so also are there manu-facturing 'levels' i n the material flow of certain i n d u s t r i a l processes. Corresponding to the accumulation of data into reports i s the accumulation of material into sub-assemblies and f i n a l products and so on. To i l l u s t r a t e the use of a matrix formulation i n generating materials requirements, four manufacturing l e v e l s are considered as l i s t e d below: Machines (Type and Model) - I, II Modules (Sub-assemblies) - A, B, C Parts - 1, 2, 3. 4 Raw Materials - a, b, c Engineering drawings give the amount of each material used i n each part. B i l l s of material give the number of parts used i n each module and the number of modules used i n each machine. The following matrices are i l l u s t r a t i v e . .Parts 146 Mo = Mo = = M a t e r i a l s\ 1 2 3 4 a 0 2 0 1 b 0 0 l 0 c 1 0 0 1 . **^Modules P a r t s ~ ~ ^ \ A B G 1 1 0 2 2 0 1 1 3 1 1 0 4 0 1 1 ,">-^Machines Module^~\^. I I I A 2 1 B 1 1 C o 1 For i n s t a n c e , p a r t No. 2 i s manufactured from two u n i t s of m a t e r i a l a and machine I i s composed of two A modules and one B module. Suppose t h a t we wish to f i n d the amount of each raw m a t e r i a l t h a t i s r e q u i r e d i n each module. To do t h i s we Mn i s : < . _ \.Modules M a t e r i a l s \ A B ' c a 0 3 3 b 1 1 0 c 1 1 3 147 Module A r e q u i r e s a u n i t o f both a and b, module B r e q u i r e s three u n i t s of a and one of both b and c, e t c . S i m i l a r l y , the number of each p a r t r e q u i r e d f o r machines I and I I can be obtained by m u l t i p l y i n g M 2 by K-^ and the amount of each raw m a t e r i a l r e q u i r e d i n both machines by m u l t i p l y i n g Mc by M 1 ( Machines ' 2 , 3 M 1 , 2 = M 2 x M l = M o d u l e s I I 1 2 3 4 2 1 3 1 1 , 3 \ M a c h i n e s M 2 ^ x M - ^ M a t e r i a l s X I 3 2 2 2 I I b c 3 3 3 6 2 5 From t h i s r e s u l t we have determined f o r example, t h a t machine I r e q u i r e s three u n i t s of each of m a t e r i a l s , a, b and c. The matrix f o r m u l a t i o n has a number of advantages, both f o r p r o c e s s i n g the i n f o r m a t i o n and f o r conceptual under-standi n g . The f u l l s c a l e m a t r i c e s f o r the company may be somewhat l a r g e f o r hand m a n i p u l a t i o n but f o r computer pro-c e s s i n g they permit ease of d a t a p r e p a r a t i o n . Each f a c t o r i s i d e n t i f i e d by i t s p o s i t i o n i n the matrix and so i t can be r e a d i l y coded. Also the requirements m a t r i x can be e a s i l y a d j u s t e d f o r d e s i g n changes. For i n s t a n c e i f module C i s added to machine I the p a r t s and m a t e r i a l requirements of machine I can be ad j u s t e d by mat r i x m u l t i p l i c a t i o n without even i n v e s t i g a t i n g the contents of module C. The matrix f o r m u l a t i o n a l s o p r o v i d e s a means of v i s u a l i z i n g the r e l a t i o n s h i p s between m a t e r i a l s , p a r t s , modules and machines from a l o g i s t i c s p o i n t of view. The e f f e c t of changing the component s t r u c t u r e of a machine on the m a t e r i a l requirements and consequently the m a t e r i a l c o s t of a machine i s e a s i l y c a l c u l a t e d . For i n s t a n c e , suppose f o r t e c h n i c a l improvements t h a t an a d d i t i o n a l module B can r e p l a c e one of the A modules i n machine I i f p a r t No. 1 i s added to module B. What e f f e c t w i l l t h i s d e s i g n change have on the m a t e r i a l requirements and m a t e r i a l c o s t of machine I? M u l t i p l i c a t i o n of the ad j u s t e d m a t r i c e s g i v e s the f o l l o w i n g r e s u l t : 1 3 a 6 6 b 3 2 c 5 5 Thus the m a t e r i a l requirements of machine I have been 149 i n c r e a s e d by 3 u n i t s of a and 2 u n i t s of c, the u n i t c o s t s of which are presumably w e l l known. The a p p l i c a t i o n of the matrix f o r m u l a t i o n to an i n t e g r a t e d system of f o r e c a s t i n g , p r o d u c t i o n s c h e d u l i n g and i n v e n t o r y c o n t r o l i s i l l u s t r a t e d by the f o l l o w i n g example, For t h i s purpose, the f o r e c a s t i n g and s c h e d u l i n g models f o r the Company are presumed to have been formulated and imple-mented. Suppose t h a t f o r e c a s t e d s a l e s f o r the next s i x months are ten of machine I and twenty of machine I I . The module requirements of t h i s f o r e c a s t are e a s i l y determined u s i n g m a t r i x M^, and m u l t i p l y i n g each element under I by 10 and under I I by 20 and adding along the rows as i l l u s t r a t e d . Machines I I I Sales F o r e c a s t 10 20 Module A 2 1 = 40 Requirements B 1 1 = 30 n 0 1 = 20 For i n s t a n c e f o r t y A modules are r e q u i r e d . Assume a l s o t h a t a p r o d u c t i o n s c h e d u l i n g model has been implemented and i t suggests one f i f t h of the module requirements should be produced i n the next two months. What are the m a t e r i a l requirements of t h i s schedule? Using matrix M, 2 we o b t a i n the f o l l o w i n g r e s u l t s 150 Modules A B c P r o d u c t i o n Schedule " 8 6 4 M a t e r i a l a 0 3 3 Requirements b 1 1 0 c 1 1 3 Thus the m a t e r i a l requirements f o r a, b and c are 20 u n i t s , 14 u n i t s and 26 u n i t s r e s p e c t i v e l y . These q u a n t i t i e s would be i n p u t s to the o r d e r i n g r u l e s f o r items a, b and c to determine how much of each should be ordered a t the present and subsequent i n v e n t o r y reviews as proposed i n the 'Inventory Study' of Chapter V. 151 APPENDIX I I I CALCULATION OF PRESENT VALUE OF PROPOSED INVENTORY CONTROL SYSTEM Costs The c o s t Items have been surmised from c o n v e r s a t i o n s on the s u b j e c t w i t h the Company's management, c o n s u l t a n t s and s e r v i c e bureau p e r s o n n e l . The c o s t of a n a l y s i s and f o r m u l a t i o n of d e c i s i o n r u l e s i s based to some extent on the work by the author i n f o r m u l a t i n g the d e c i s i o n r u l e s f o r the seven items. B e n e f i t s The estimate of the reduced c o s t s of i n v e n t o r y opera-t i o n are based on p r o s p e c t i v e savings through reduced i n v e n t o r y l e v e l s minus the a d d i t i o n a l o r d e r i n g c o s t s as i n d i c a t e d by the s i m u l a t i o n r e s u l t s f o r the seven items t h a t have been studies'*". C a l c u l a t i o n The net present value i s c a l c u l a t e d u s i n g a three year time h o r i z o n and a twelve per cent r a t e f o r d i s c o u n t i n g f u t u r e b e n e f i t s and c o s t s , t h a t i s , items 5 and 6 . iThe d e t a i l e d c a l c u l a t i o n can not be d i s p l a y e d w i t h -out d i v u l g i n g c o n f i d e n t i a l i n f o r m a t i o n . 152 TABLE XII NET PRESENT VALUE CALCULATION OP THE PROPOSED INVENTORY CONTROL SYSTEM Item D e s c r i p t i o n Cost(ft) B e n e f i t ( $ ) Present - V a l u e (|) 1. Inventory system share of #2,000 $ 2,000 d e v e l o p i n g a m a t e r i a l r e q u i r e -ments system - E n g i n e e r i n g Dept. 2. A n a l y s i s of requirements and f o r m u l a t i o n of d e c i s i o n r u l e s - s t a f f and c o n s u l t a n t - up to present - remaining items 3. Developing a new i n v e n t o r y i n f o r m a t i o n system - s t a f f 4. Programming system f o r e l e c -t r o n i c data p r o c e s s i n g - computer s e r v i c e bureau 5. Annual c o s t of key punching and e l e c t r o n i c d a t a p r o c e s s i n g 6 . Estimated annual b e n e f i t s i n terms of reduced i n v e n t o r y c o s t s . Net Present Value $ 9,500 $1,000 $7,000 $1,000 1,000 7,000 $3,000 $ 3,000 $6,000 $15,000 M.5,00.0 $37,500 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0093552/manifest

Comment

Related Items